Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 24

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Earn 100

Which of the following limits is/are unity?

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Important Questions on Limits

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 25

If

f (x) = \{\begin{cases} \frac{\sin [x]}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}

where

[x]

denotes the greatest integer less than or equal to

x

, 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-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 14

If

\underset{x \to \infty}{Lim} [\sqrt{x^{2} - 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 15

If

\underset{x \to 0}{Lim} \frac{a \sin x - \sin 2 x}{\tan^{3} x} = ℓ

(finite), then find the value of

(a + ℓ)

.

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 16

Evaluate

\underset{n \to \infty}{Lim} (\frac{1}{\sqrt{n^{2}}} + \frac{1}{\sqrt{n^{2} + 1}} + \frac{1}{\sqrt{n^{2} + 2}} + \dots \dots . . + \frac{1}{\sqrt{n^{2} + 2 n}})

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-3>Q 17

Evaluate

\underset{x \to 0}{Lim} [\frac{5 \sin x}{x}] + \underset{x \to 0}{Lim} [\frac{5 \tan x}{x}]

where

[*]

denotes the greater function.