ESE 2021 Technical Quiz || "Multivariable Calculus Limits, Continuity and Differentiability"

The limit of the function will be:

Determine the coordinates of the point which is on the parabola  and which is closest to the straight line y = 3x -3 are

In the mean value theorem f(b) – f(a) = (b – a) f’(c) where c is lying between a and b. Find the value of c, if f(x) = x(x – 1) (x – 2), a = 0 and .

A function is expressed as:

f(x) =

The values of a, b, and c respectively for which function will be continuous and differentiable everywhere.

 is: