JEE Main Continuity and Differentiability — practice questions
17 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Continuity and Differentiability in the app →A function $f$ is continuous at a point $c$ if:The derivative of $e^x$ with respect to $x$ is:The derivative of $\log_e x$ with respect to $x$ is:By the chain rule, $\dfrac{d}{dx} f(g(x))$ equals:The function $f(x) = |x|$ is continuous everywhere but is NOT differentiable at:Every differentiable function is necessarily:The derivative of $e^{2x}$ with respect to $x$ is:The derivative of $\log_e(x^2)$ with respect to $x$ is:A function $f$ is continuous at $c$ only if the left-hand limit, right-hand limit and $f(c)$ are:The derivative of $x e^x$ with respect to $x$ is:Rolle's theorem requires that $f$ be continuous on $[a,b]$, differentiable on $(a,b)$ and:The derivative of $\tan x$ with respect to $x$ is:The derivative of $ qrt{x}$ with respect to $x$ is:A function $f$ is continuous at $x = a$ if:A function differentiable at $x = a$ is always:The derivative of $ in(3x)$ is:Rolle's theorem applies to a function $f$ on $[a, b]$ if $f$ is: