Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If the function $f colon R rightwards arrow R$ be defined by $f open parentheses x close parentheses equals tan invisible function application x minus x$ , then $f left parenthesis x right parenthesis$

Increases
Decreases
Remains constant
Becomes zero

The correct answer is: Increases

$because blank f open parentheses x close parentheses equals tan invisible function application x minus x$
On differentiating w.r.t. $x$ , we get

$f to the power of ´ end exponent open parentheses x close parentheses equals sec to the power of 2 end exponent invisible function application x minus 1 equals fraction numerator 1 over denominator cos to the power of 2 end exponent invisible function application x end fraction minus 1 equals fraction numerator 1 minus cos to the power of 2 end exponent invisible function application x over denominator cos to the power of 2 end exponent invisible function application x end fraction$

Since, $0 less or equal than cos to the power of 2 end exponent invisible function application x less or equal than 1$ for all values of $x$

$therefore f to the power of ´ end exponent open parentheses x close parentheses greater than 0$ for all values of $x$ . Thus, $f left parenthesis x right parenthesis$ always increases

Related Questions to study

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ , at $x equals 1$ is

The slope of the tangent to the curve $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$ , at $x equals 1$ is

The function $f open parentheses x close parentheses equals log subscript e end subscript invisible function application open parentheses x to the power of 3 end exponent plus square root of x to the power of 6 end exponent plus 1 end root close parentheses$ is of the following types:

The function $f open parentheses x close parentheses equals log subscript e end subscript invisible function application open parentheses x to the power of 3 end exponent plus square root of x to the power of 6 end exponent plus 1 end root close parentheses$ is of the following types:

For the curve $y equals x blank e to the power of x end exponent$ , the point

For the curve $y equals x blank e to the power of x end exponent$ , the point

parallel

If the semi-vertical angle of a cone is $45 degree$ , then the rate of change of volume of the cone is

If the semi-vertical angle of a cone is $45 degree$ , then the rate of change of volume of the cone is

Let $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 end subscript close parentheses equals g open parentheses x subscript 0 end subscript close parentheses comma f to the power of ´ end exponent open parentheses x close parentheses greater than g ´ left parenthesis x right parenthesis$ for $x greater than x subscript 0 end subscript comma$ then

Let $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 end subscript close parentheses equals g open parentheses x subscript 0 end subscript close parentheses comma f to the power of ´ end exponent open parentheses x close parentheses greater than g ´ left parenthesis x right parenthesis$ for $x greater than x subscript 0 end subscript comma$ then

The equation of the normal line to the curve $y equals x log subscript e end subscript invisible function application x$ parallel to $2 x minus 2 y plus 3 equals 0$ is

The equation of the normal line to the curve $y equals x log subscript e end subscript invisible function application x$ parallel to $2 x minus 2 y plus 3 equals 0$ is

parallel

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ which is equal to

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ which is equal to

The length of subtangent to the curve $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$ at the point $left parenthesis negative a comma blank a right parenthesis$ is

The length of subtangent to the curve $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$ at the point $left parenthesis negative a comma blank a right parenthesis$ is

A ray of light is incident along vector $fraction numerator 1 over denominator square root of 2 end fraction i with not stretchy hat on top minus fraction numerator 1 over denominator square root of 2 end fraction j with not stretchy hat on top plus k with not stretchy hat on top$ on plane mirror placed in XY-plane normal on incidence point is along Z-axis

A ray of light is incident along vector $fraction numerator 1 over denominator square root of 2 end fraction i with not stretchy hat on top minus fraction numerator 1 over denominator square root of 2 end fraction j with not stretchy hat on top plus k with not stretchy hat on top$ on plane mirror placed in XY-plane normal on incidence point is along Z-axis

parallel

$text If end text a equals 3 i with not stretchy hat on top plus 4 j with not stretchy hat on top text and end text b equals 4 i with not stretchy hat on top minus 3 j with not stretchy hat on top comma text then end text$

$text If end text a equals 3 i with not stretchy hat on top plus 4 j with not stretchy hat on top text and end text b equals 4 i with not stretchy hat on top minus 3 j with not stretchy hat on top comma text then end text$

If unit vector $a equals a subscript 1 i with not stretchy hat on top plus a subscript 2 j with not stretchy hat on top plus a subscript 3 k with not stretchy hat on top$ . The possible values of a₁ a₂ and a₃ are

If unit vector $a equals a subscript 1 i with not stretchy hat on top plus a subscript 2 j with not stretchy hat on top plus a subscript 3 k with not stretchy hat on top$ . The possible values of a₁ a₂ and a₃ are

Current from $A blank a n d blank B$ in the straight wire is decreasing. The direction of induced current in the loop, is

Current from $A blank a n d blank B$ in the straight wire is decreasing. The direction of induced current in the loop, is
Physics-General

parallel

According to Lenz’s law of electromagnetic induction

According to Lenz’s law of electromagnetic induction

Physics-General

Two circular coils $A$ and $B$ are facing each other as shown in figure. When the current $i$ through $A$ is altered

Two circular coils $A$ and $B$ are facing each other as shown in figure. When the current $i$ through $A$ is altered
Physics-General

A circular loop of radius $R$ , carrying current $I$ lies in $x y minus$ plane with its centre at origin. The total magnetic flux through $x y$ -plane is

A circular loop of radius $R$ , carrying current $I$ lies in $x y minus$ plane with its centre at origin. The total magnetic flux through $x y$ -plane is

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.