JEE Main · Mathematics

Limits, continuity and differentiability

13 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 13 questions

What is the value of the limit $lim_{x \to 0} \frac{s i n ( 3 x ) - t a n ( 2 x )}{x}$ ?
What is the value of the limit $lim_{x \to 0} \frac{1 - c o s ( 4 x )}{x ^{2}}$ ?
If the function $f (x) = {\frac{s i n ( 5 x )}{2 x}, k, x \neq = 0 x = 0$ is continuous at $x = 0$ , what is the value of $k$ ?
What is the value of the limit $lim_{x \to \infty} (1 + \frac{3}{x})^{2 x}$ ?
What is the derivative of $f (x) = ln (sec x + tan x)$ with respect to $x$ ?
If a curve is given parametrically by $x = a (θ - sin θ)$ and $y = a (1 - cos θ)$ , what is the value of $\frac{d y}{d x}$ at $θ = \frac{π}{2}$ ?
At how many points in $R$ is the function $f (x) = ∣ x - 2∣ + ∣ x - 3∣$ not differentiable?
What is the value of the limit $lim_{x \to 0} \frac{e ^{x^{2}} - c o s x}{x ^{2}}$ ?
At what point does the cubic function $f (x) = x^{3} - 6 x^{2} + 9 x + 15$ attain its local minimum?
What is the value of the limit $lim_{x \to 0} \frac{1 + x - 1 - x}{x}$ ?
If $y = tan^{- 1} (\frac{1 + x ^{2} - 1}{x})$ for $x \neq = 0$ , what is the derivative $\frac{d y}{d x}$ ?
Let $f (x) = {a x^{2} + 1, 2 x + b, x \leq 1 x > 1$ . If $f (x)$ is differentiable at $x = 1$ , what are the values of constants $a$ and $b$ ?
What is the value of the limit $lim_{x \to 0} \frac{l n ( 1 + 2 x )}{s i n ( 3 x )}$ ?

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