AP EAPCET (Engineering) Continuity and Differentiability — practice questions
18 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Continuity and Differentiability in the app →If f and g are both continuous at a point c, then f + g isFor continuous f and g, the quotient f/g is continuous at every point whereIf a function is differentiable at a point c, what must be true at c?The function f(x) = |x| at x = 0 isFor x > 0, the derivative of log x (natural logarithm) isWhat is the domain of the logarithm function to a base b > 1?Which point always lies on the curve y = b^x for any base b > 1?Since 2^3 = 8, the value of log to base 2 of 8 isThe quotient rule gives the derivative of u/v, for v nonzero, asIf f = v(t) and t = u(x), the chain rule gives df/dx asTaking natural logs of y = [u(x)]^v(x) gives log y equal toA function equals (x^2 - 9)/(x - 3) for x not equal to 3 and has value k at x = 3. It is continuous at 3 when Let f(x) = kx^2 for x <= 2 and f(x) = 3 for x > 2. For continuity at x = 2, the value of k isIf x^2 + y^2 = 1, implicit differentiation gives dy/dx equal toFor x > 0, logarithmic differentiation shows that the derivative of x^x isThe greatest integer function [x] is discontinuous at which of these points?The function f(x) = 1/(x - 2) is discontinuous atThe identity x = e^(log x) holds only for