TS EAPCET (Engineering) Continuity and Differentiability — practice questions
32 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Continuity and Differentiability in the app →If y = x^4, what is the second order derivative d2y/dx2?For y = x^5, find d2y/dx2.If y = log x (natural logarithm), then d2y/dx2 isIf y = 3x^2 + 2x, what is d2y/dx2?If x = t^2 and y = t^3, find dy/dx.If x = a cos(theta) and y = a sin(theta), then dy/dx isFind dy/dx for y = x^(sin x), x > 0.Logarithmic differentiation is valid for [u(x)]^v(x) only when u(x) isWhich type of function is best handled by logarithmic differentiation?The derivative of the natural exponential function e^x isDifferentiate y = x sin x.Differentiate y = (sin x)/x for x not equal to 0.On x^2 + y^2 = 4, the slope dy/dx at the point (0, 2) isThe function f(x) = |x| at x = 0 isContinuity of f at a point is a ___ for differentiability there.Sum, difference and product of two continuous functions are alwaysThe quotient f/g of continuous functions is continuous whereverThe numerator of the quotient rule for (u/v)' isIf f = v o u and t = u(x), the chain rule gives df/dx =The greatest integer function f(x) = [x] is discontinuous atThe second order derivative of y = f(x) is written in Leibnitz form asSecond order derivative of f(x) exists only ifDomain of the exponential function y = b^x with b > 1 isFor every base b > 1, the curve y = b^x passes throughThe logarithm to base e is called theThe exponential function y = e^x is known as theAn exponential function with base 10 is called theIf x = f(t) and y = g(t), the variable t is called aFor x = f(t), y = g(t), dy/dx equals (dx/dt not zero)If y = e^(3x), then d2y/dx2 isWhich notation does NOT denote the second order derivative of y = f(x)?If a function is discontinuous at c, then it is ___ at c.