Mathematics Sessional Examination

Find the limits of limx-1(x³ + x² + x)¹00.

For what values of x, if any, is the function f(x) = e3x-e2x / x²-16 discontinuous?

Find Dn (x).

Is the function x differentiable at x=0?

Write the cauchy's form of remainder after n-terms in Taylor's Theorem.

Find limx→0 X.

Show that the function f(x)=x+|x-1|+|x-2| is continuous at the points x=0,1,2.

Show that f(x) is discontinuous at x=1/2.

Verify the Roll's Theorem for the function f(x) = x³ - 4x on [-2,2].

Write the geometrical interpretation of Lagrange's Mean Value Theorem.