Explore topic-wise MCQs in Differential and Integral Calculus Questions and Answers.

This section includes 4 Mcqs, each offering curated multiple-choice questions to sharpen your Differential and Integral Calculus Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.

Expansion of \(f (x,y) = tan^{-1} \frac{⁡y}{x}\) upto first degree containing (x+1) & (y-1) is __________

A. \(\frac{3π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{2} + \frac{(y-1)^2}{2!} \frac{1}{2}\)
B. \(\frac{π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\)
C. \(\frac{5π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\)
D. \(\frac{3π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\)
Answer» B. \(\frac{π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\)
Discussion
2.

Taylor’s theorem is mainly used in expressing the function as sum with infinite terms.

A. True
B. False
Answer» B. False
Discussion
3.

Given f (x,y)=sin⁡xy, what is the value of the third degree first term in Taylor’s series near (1,-\(\frac{π}{2}\)) where it is expanded in increasing order of degree & by following algebraic identity rule?

A. \(\frac{π^3}{8}\)
B. \(\frac{π^3}{8} \frac{(x-1)(y+\frac{π}{2})}{3!}\)
C. 0
D. \(-\frac{π^3}{8} \frac{(x-1)^3}{3!}\)
Answer» D. \(-\frac{π^3}{8} \frac{(x-1)^3}{3!}\)
Discussion
4.

Given f (x,y)=ex cos⁡y, what is the value of the fifth term in Taylor’s series near (1,\(\frac{π}{4}\)) where it is expanded in increasing order of degree & by following algebraic identity rule?

A. \(\frac{-e(x-1)(y-\frac{π}{4})}{\sqrt{2}}\)
B. \(-\sqrt{2} e(x-1)(y-\frac{π}{4})\)
C. \(\frac{e(x-1)^2}{\sqrt{2}}\)
D. \(\frac{e(y-\frac{π}{4})^2}{\sqrt{2}}\)
Answer» B. \(-\sqrt{2} e(x-1)(y-\frac{π}{4})\)
Discussion