UP Board Class 12 Limits and Continuity — practice questions
24 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice UP Board Class 12 Limits and Continuity in the app →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:A function whose graph can be drawn without lifting the pen is:If f is not continuous at c, then c is called a point of:Which new class of functions does this chain introduce?If a function is differentiable at a point, it is also:The rule for differentiating a composite function is the:f(x) = x squared at x = 0 is:Functions written with y not isolated are called:Continuity of f at c requires the limit at c to equal:Theorem 1 concerns two functions that are both:Theorem 2 deals with which kind of function?Theorem 3 says differentiability at a point implies:Does continuity at a point guarantee differentiability?The chain rule can be extended to composites of:An alternative to repeated product rule for many factors is:For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:The function f(x) = |x| at x = 0 is continuous but not:To differentiate an implicit relation you use the:A function that fails the limit test at a point is:Composites of continuous functions, by Theorem 2, are:Two things this chain introduces beside continuity are differentiability and: