Differential Calculus Mock Tests

The derivative of x³ at x = 2 is:

The Taylor series expansion of eˣ about x = 0 is:

The derivative of e^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:

Rolle's theorem applies to f(x) = x² − 4x + 3 on the interval [1, 3]. The value of c guaranteed by the theorem is:

If f(x) = x³ - 3x² + 2x, then f'(1) equals:

The value of lim(x→0) (sin(3x)/x) is:

The limit as x approaches 0 of sin(x)/x is: