Differential Calculus Mock Tests

Rolle's theorem is applicable to f(x) = x² - 4x + 3 on the interval [1, 3] because:

The Maclaurin series expansion of eˣ up to the third term is:

The value of lim(x→0) (sin x)/x is:

The derivative of sin(2x) with respect to x is:

Mean Value Theorem applies to f(x) = x³ on [1, 2]. The value of c in (1, 2) such that f'(c) = (f(2) − f(1))/(2 − 1) is:

The function f(x) = |x − 2| is not differentiable at:

The Taylor series expansion of e^x about x = 0 up to the term in x^3 is:

The derivative of xˣ with respect to x is: