Solution for the question - if f(x) has a derivative at x=a, then lim_(x rarr a)(xf(a)-af(x))/(x-a)isequal to af(a)+f^(')(a) '/> f(a)+f(a) '/> af(a)-f^(')(a) '/>

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Question

If $f left parenthesis x right parenthesis$ has a derivative at $x equals a text , then end text lim for x not stretchy rightwards arrow a of fraction numerator x f left parenthesis a right parenthesis minus a f left parenthesis x right parenthesis over denominator x minus a end fraction$ is equal to

$f (a) - a f^{'} (a)$
$a f (a) - f^{'} (a)$
$f (a) + f^{'} (a)$
$af (a) + f^{'} (a)$

The correct answer is: $f left parenthesis a right parenthesis minus a f to the power of straight prime left parenthesis a right parenthesis$

$lim for x not stretchy rightwards arrow a of fraction numerator x f left parenthesis a right parenthesis minus a f left parenthesis x right parenthesis over denominator x minus a end fraction$
$equals lim for x not stretchy rightwards arrow a of fraction numerator x f left parenthesis a right parenthesis minus af invisible function application left parenthesis a right parenthesis minus a f left parenthesis x right parenthesis plus af invisible function application left parenthesis a right parenthesis over denominator x minus a end fraction$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals lim for x not stretchy rightwards arrow a of fraction numerator f left parenthesis a right parenthesis left parenthesis x minus a right parenthesis minus a left square bracket f left parenthesis x right parenthesis minus f left parenthesis a right parenthesis right square bracket over denominator x minus a end fraction end cell row cell equals lim for x not stretchy rightwards arrow a of fraction numerator f left parenthesis a right parenthesis left parenthesis x minus a right parenthesis over denominator x minus a end fraction minus a lim for x not stretchy rightwards arrow a of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis a right parenthesis over denominator left parenthesis x minus a right parenthesis end fraction end cell row cell equals f left parenthesis a right parenthesis minus a f to the power of straight prime left parenthesis a right parenthesis end cell end table$

The value of $fraction numerator d over denominator d x end fraction open square brackets open parentheses fraction numerator tan squared invisible function application 2 x minus tan squared invisible function application x over denominator 1 minus tan squared invisible function application 2 x tan squared invisible function application x end fraction close parentheses cot invisible function application 3 x close square brackets$ is

maths-General

General

maths-

The derivative of $e to the power of x cubed end exponent$ with respect to log is

maths-General

General

maths-

The derivative of $sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 x over denominator 1 plus x squared end fraction close parentheses$ with respect to $cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 minus x squared over denominator 1 plus x squared end fraction close parentheses$ is

maths-General

General

maths-

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

maths-General

General

maths-

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

maths-General

General

Maths-

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

Maths-General

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

General

maths-

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

maths-General

General

maths-

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

maths-General

General

maths-

The domain of the function $f open parentheses x close parentheses equals fraction numerator sin to the power of 1 end exponent invisible function application left parenthesis x minus 3 right parenthesis over denominator square root of 9 minus x to the power of 2 end exponent end root end fraction$ is

maths-General

General

maths-

Let $f open parentheses x close parentheses equals fraction numerator 1 over denominator 2 end fraction minus tan invisible function application open parentheses fraction numerator pi x over denominator 2 end fraction close parentheses$ , $negative 1 less than x less than 1$ and $g open parentheses x close parentheses equals square root of 3 plus 4 x minus 4 x to the power of 2 end exponent end root$ , then dom $left parenthesis f plus g right parenthesis$ is given by

maths-General

General

physics-

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

physics-General

General

chemistry-

Select the rate law that correspond to the data shown for the following reaction.

chemistry-General

General

chemistry-

Select the rate law that corresponds to the data shown for the following reaction.

chemistry-General

General

maths-

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

maths-General

General

physics-

Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle $theta$ under the influence of magnets. The ratio of distances d₁ and d₂ will be

physics-General

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$f (a) - a f^{'} (a)$
$a f (a) - f^{'} (a)$
$f (a) + f^{'} (a)$
$af (a) + f^{'} (a)$

The correct answer is: $f left parenthesis a right parenthesis minus a f to the power of straight prime left parenthesis a right parenthesis$

Related Questions to study

The derivative of $e to the power of x cubed end exponent$ with respect to log is

The derivative of $e to the power of x cubed end exponent$ with respect to log is

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

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If has a derivative at is equal to

The correct answer is:

Related Questions to study

The value of is

The value of is

The derivative of with respect to log is

The derivative of with respect to log is

The derivative of with respect to is

The derivative of with respect to is

The rate of change of with respect to at is

The rate of change of with respect to at is

If then is

If then is

If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

The domain of the function is

The domain of the function is

Range of the function is

Range of the function is

The domain of the function is

The domain of the function is

Let , and , then dom is given by

Let , and , then dom is given by

In the adjacent diagram, represents a wavefront and and , the corresponding two rays. Find the condition on for constructive interference at P between the ray and reflected ray

In the adjacent diagram, represents a wavefront and and , the corresponding two rays. Find the condition on for constructive interference at P between the ray and reflected ray

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

is relation on given by Which of the following belongs to ?

is relation on given by Which of the following belongs to ?

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The correct answer is: $f left parenthesis a right parenthesis minus a f to the power of straight prime left parenthesis a right parenthesis$

The derivative of $e to the power of x cubed end exponent$ with respect to log is

The derivative of $e to the power of x cubed end exponent$ with respect to log is

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?