AIEEE 2002 | Limits, Continuity and Differentiability Question 200 | Mathematics

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AIEEE 2002

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}$$ is

$$1$$

$$-1$$

zero

does not exist

AIEEE 2002

MCQ (Single Correct Answer)

-1

Let $$f(2) = 4$$ and $$f'(x) = 4.$$

Then $$\mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \over {x - 2}}$$ is given by

$$2$$

$$- 2$$

$$- 4$$

$$3$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{n \to \infty } {{{1^p} + {2^p} + {3^p} + ..... + {n^p}} \over {{n^{p + 1}}}}$$ is

$${1 \over {p + 1}}$$

$${1 \over {1 - p}}$$

$${1 \over p} - {1 \over {p - 1}}$$

$${1 \over {p + 2}}$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$

$${e^4}$$

$${e^2}$$

$${e^3}$$

$$1$$

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