Explore topic-wise MCQs in Differential Calculus.

This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Differential Calculus knowledge and support exam preparation. Choose a topic below to get started.

1.

Maclaurin’s Theorem is a special type of Taylor’s Theorem.

A. False
B. True
Answer» C.
Discussion
2.

For the power series of the form, \(∑_{i=0}^∞ a_i z^i,\) which one of the following may not be true?

A. The series converges only for z=0
B. The series converges absolutely for all z
C. The series converges absolutely for all z in some finite open interval (-R, R) and diverges if z<-R or z>R
D. At the points z=R and z=-R, the series will diverge
Answer» E.
Discussion
3.

The initial condition for the recurrence relation of a factorial is ___________

A. 0!=0
B. 0!=1
C. 1!=1
D. 1!=0
Answer» C. 1!=1
Discussion
4.

What is the first term in the Taylor series expansion of f(x) = 8x5-3x2-5x about x=2?

A. 232
B. 244
C. 234
D. 222
Answer» D. 222
Discussion
5.

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
Answer» B. False
Discussion
6.

Lagrange’s Remainder for Maclaurin’s Theorem is given by _____________

A. \(\frac{x^n}{(n-1)!}f^{(n)}(θx) \)
B. \(\frac{x^n}{n!} f^{(n)}(θx)\)
C. \(\frac{x^{n-1}}{n!} f^{(n)}(θx)\)
D. \(\frac{x^n}{n!}f^{(n-1)}(θx)\)
Answer» C. \(\frac{x^{n-1}}{n!} f^{(n)}(θx)\)
Discussion
7.

Taylor’s theorem was stated by the mathematician _____________

A. Brook Taylor
B. Eva Germaine Rimington Taylor
C. Sir Geoffrey Ingram Taylor
D. Michael Eugene Taylor
Answer» B. Eva Germaine Rimington Taylor
Discussion