Question

Cauchy’s Remainder for Maclaurin’s Theorem is given by  \(\frac{x^n(1-θ)^{n-1}}{(n-1)!}f^{(n)}(θx)\).

(a) True

(b) False

This question was posed to me at a job interview.

I need to ask this question from Generalized Mean Value Theorem in chapter Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (a) True

To explain: Schlomilch’s Remainder for Maclaurin’s Theorem is given by, \(\frac{x^n(1-θ)^{n-p}}{(n-1)!p} f^{(n)}(θx).\)

To obtain Cauchy’s Remainder for Maclaurin’s Theorem, we put p=1, which gives us,

\(\frac{x^n(1-θ)^{n-1}}{(n-1)!}f^{(n)}(θx).\)