Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 32

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If $f (x)$ be a differentiable function such that $f^{'} (3) = 60$ and $f^{'} (2) = 3$ then $\lim_{h \to 0} \frac{f (h^{3} + 5 h + 3) - f (3)}{f (4 h - 2 h^{2} + 2) - f (2)}$ is equal to

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Important Questions on Limits and Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 33

Let $\lim_{n \to \infty} n (\sqrt[3]{n^{3} + 6 n^{2} + 3 n + 2} + \sqrt{n^{2} - 4 n + 2} - 2 n) = \frac{p}{q}$ where $p$ and $q$ are coprime then the value of $p + q$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 7

If

f (x) = 2 - \sqrt{25 - x^{2}}

, then

\lim_{x \to 1} \frac{f (x) - f (1)}{x - 1}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 10

If

f

be a function of

' x'

such that

f (9) = 9, f^{'} (9) = 3

, then

\lim_{x \to 9} \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 18

The value of

\lim_{x \to 0} (1 - \frac{1}{2^{x}}) (\frac{1}{\sqrt{\tan x + 4} - 2})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 19

If

\lim_{x \to 0} \frac{\sin 6 x}{\tan 3 x} = a, \lim_{x \to \infty} \frac{\sin x}{x} = b, \lim_{x \to \infty} \frac{\log x}{x} = c

then value of

a + b + c

is

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 20

Let

a = \lim_{x \to 0} x \cot x

and

b = \lim_{x \to 0} x \log x

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 23

Let

f (2) = 4, f^{'} (2) = 4

. Then

{Lt}_{x \to 2} \frac{x f (2) - 2 f (x)}{x - 2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 24

Let

α

and

β

be the distinct roots of

a x^{2} + b x + c = 0

, then

\lim_{x \to a} \frac{1 - \cos (a x^{2} + b x + c)}{(x - α)^{2}}

is equal to