Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 42

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If the value of $\lim_{x \to 0} \frac{{(1 + \sin x)}^{cosec x} - e + (\frac{\sin x}{2}) e}{\sin^{2} x}$ is $k$ , then $(24 k - 11 e)$ 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 46

Let

S_{n} = \frac{1}{1 \cdot 4} + \frac{1}{4 \cdot 7} + \frac{1}{7 \cdot 10} + \dots

to

n

terms then

\lim_{n \to \infty} S_{n}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 47

Let

t_{r} = \frac{r}{1 + r^{2} + r^{4}}

, then

\lim_{n \to \infty} \sum_{r = 1}^{n} t_{r}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 48

Suppose

f (x)

is differentiable at

x = 1

and

\underset{n \to 0}{L t} \frac{1}{n} f (1 + n) = 5

, then

f^{'} (1)

equals -

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 49

If

f (x)

and

g (x)

are differentiable functions and

f (1) = g (1) = 2

, then

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

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 1

The value of

\lim_{h \to 0} \{\frac{1}{h \cdot (8 + h)^{1 / 3}} - \frac{1}{2 h}\}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 2

The value of

\lim_{x \to \frac{π}{2}} \frac{\{1 - \tan \frac{x}{2}\} {1 - \sin x}}{\{1 + \tan \frac{x}{2}\} (π - 2 x)^{3}}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 3

The value of

\lim_{x \to 0} | x |^{[\cos x]}

is ;

{[\cdot] =

GIF

}

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Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 4

\lim_{x \to \infty} \frac{x^{4} \sin (\frac{1}{x}) + x^{2}}{1 + |x^{3}|}

equals