Maths-

General

Easy

Question

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction equals$

4
$2 \sqrt{2}$
$\frac{1}{\sqrt{2}}$
$\sqrt{2}$

hint Hint:

In the question we will use L hospital theorem, $fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction$ .

The correct answer is: 4

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction u sin g space L h o s p i t a l space t h e o r e m comma space equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style x over denominator begin display style fraction numerator d blank over denominator d x end fraction end style square root of x plus 4 end root minus 2 end fraction equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator 2 square root of x plus 4 end root end fraction end style end fraction equals L t subscript x not stretchy rightwards arrow 0 end subscript 2 square root of x plus 4 end root equals 2 square root of 0 plus 4 end root equals 2 cross times 2 equals 4$

$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator cube root of 1 plus x end root minus cube root of 1 minus x end root over denominator x end fraction equals$

Maths-General

General

Maths-

If $f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root comma text then end text L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals$

Maths-General

General

maths-

$L t subscript x not stretchy rightwards arrow 2 end subscript open parentheses fraction numerator square root of 1 minus cos space left curly bracket 2 left parenthesis x minus 2 right parenthesis factorial end root over denominator x minus 2 end fraction close parentheses equals$

maths-General

General

Maths-

If $L t subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses 1 plus a over x plus b over x squared close parentheses to the power of 2 x end exponent equals e squared$ then the values of a and b are

Maths-General

General

Maths-

$text In end text straight triangle A B C comma straight capital sigma fraction numerator a squared sin invisible function application left parenthesis B minus C right parenthesis over denominator sin invisible function application A end fraction equals$

Maths-General

General

Maths-

If $L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log begin display style space end style left parenthesis 3 plus x right parenthesis minus log space left parenthesis 3 minus x right parenthesis over denominator x end fraction equals k$ then k=

Maths-General

General

maths-

Let $proportional to$ and $beta$ be the distinct roots of $a x squared plus b x plus c equals 0$ then $fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction$

maths-General

General

Maths-

In $straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals$

Maths-General

General

maths-

$Lt subscript x not stretchy rightwards arrow 1 end subscript space left parenthesis 1 minus x right parenthesis tan space open parentheses pi x over 2 close parentheses equals$

maths-General

General

Maths-

In $straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow pi over 2 end subscript space fraction numerator open square brackets 1 minus tan space x over 2 close square brackets left square bracket 1 minus sin space x right square bracket over denominator open square brackets 1 plus tan space x over 2 close square brackets left square bracket pi minus 2 x right square bracket cubed end fraction equals$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator square root of a plus 2 x end root minus square root of 3 x end root over denominator square root of 3 a plus x end root minus 2 square root of x end fraction equals$

Maths-General

General

Maths-

In $straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow 1 end subscript fraction numerator left parenthesis 2 x minus 3 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator 2 x squared plus x minus 3 end fraction equals$

Maths-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction$

Maths-General

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4

In the question we will use L hospital theorem, .

The correct answer is: 4

Related Questions to study

If

If

If then the values of a and b are

If then the values of a and b are

If then k=

If then k=

Let and be the distinct roots of then

Let and be the distinct roots of then

In

In

In

In

In

In

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4
$2 \sqrt{2}$
$\frac{1}{\sqrt{2}}$
$\sqrt{2}$

If $L t subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses 1 plus a over x plus b over x squared close parentheses to the power of 2 x end exponent equals e squared$ then the values of a and b are

If $L t subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses 1 plus a over x plus b over x squared close parentheses to the power of 2 x end exponent equals e squared$ then the values of a and b are

If $L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log begin display style space end style left parenthesis 3 plus x right parenthesis minus log space left parenthesis 3 minus x right parenthesis over denominator x end fraction equals k$ then k=

If $L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log begin display style space end style left parenthesis 3 plus x right parenthesis minus log space left parenthesis 3 minus x right parenthesis over denominator x end fraction equals k$ then k=

In $straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals$

In $straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals$

In $straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals$

In $straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals$

In $straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals$

In $straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals$