WB JEE 2010 | Limits, Continuity and Differentiability Question 12 | Mathematics

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

If $$y = (1 + x)(1 + {x^2})(1 + {x^4})\,.....\,(1 + {x^{2n}})$$, then the value of $${\left( {{{dy} \over {dx}}} \right)_{x = 0}}$$ is

$$-$$1

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

The value of f(0) so that the function $$f(x) = {{1 - \cos (1 - \cos x)} \over {{x^4}}}$$ is continuous everywhere is

$${1 \over 2}$$

$${1 \over 4}$$

$${1 \over 6}$$

$${1 \over 8}$$

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

$$\mathop {\lim }\limits_{x \to 0} {{\sin |x|} \over x}$$ is equal to

positive infinity

does not exist

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

In which of the following functions, Rolle's theorem is applicable?

f(x) = | x | in $$-$$2 $$\le$$ x $$\le$$ 2

f(x) = tanx in 0 $$\le$$ x $$\le$$ $$\pi$$

f(x) = 1 + (x $$-$$ 2)^2/3 in 1 $$\le$$ x $$\le$$ 3

f(x) = x(x $$-$$ 2)² in 0 $$\le$$ x $$\le$$ 2

WB JEE Subjects