Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 26

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Earn 100

Which of the following limits vanishes?

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Important Questions on Limits

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 27

{Lim}_{x \to 0^{+}} ((x^{x^{x}}) - x^{x})

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 28

Let

ℓ = {Lim}_{x \to 0} x^{m} (ℓ n x)^{n}

where

m, n \in N

then -

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 30

If

g (x)

is a polynomial satisfying

g (x) g (y) = g (x) + g (y) + g (x y) - 2

for all real

x

and

y

and

g (2) = 5

then

g (3)

is equal to-

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 31

Let

n

be an odd integer. If

\sin n θ = \sum_{r = 0}^{n} b_{r} \sin^{r} θ

, for every value of

θ

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 11

Evaluate

\underset{x \to 1}{Lim} \frac{\sqrt[13]{x} - \sqrt[7]{x}}{\sqrt[5]{x} - \sqrt[3]{x}}

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 12

Evaluate

\underset{x \to 1}{Lim} \frac{[\sum_{k = 1}^{100} x^{k}] - 100}{x - 1}

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 13

If

\underset{x \to \infty}{Lim} [\frac{x^{2} + 1}{x + 1} - a x - b] = 0

, then find

a + b

.

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 14

If

\underset{x \to \infty}{Lim} [\sqrt{x^{2} - x + 1} - a x - b] = 0

, then find

a - b