Explore topic-wise MCQs in Differential Calculus.

This section includes 6 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.

Half Range Fourier Series contains either sine or cosine terms.

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

Given ( _0^8 x^{ frac{1}{3}} dx, ) find the error in approximating the integral using Simpson s ( frac{1}{3} ) Rule with n=4.

A. 1.8
B. 2.9
C. 0.3
D. 0.35
Answer» E.
Discussion
3.

What is the derivative of ( frac{3x^2}{(1-sinx)} )?

A. ( frac{6xsinx-3x^2 cosx}{(1-sinx)^2} )
B. ( frac{6x}{1-sinx} )
C. ( frac{6xsinx-3x^2 cosx-6x}{(1-sinx)^2} )
D. ( frac{6xsinx-3cosx-6}{(1-sinx)^2} )
Answer» D. ( frac{6xsinx-3cosx-6}{(1-sinx)^2} )
Discussion
4.

Product Rule of the derivative is given by ________

A. ( frac{d(fg)}{dx}= frac{d(g)}{dx}* frac{d(f)}{dx} )
B. ( frac{df}{dx}* frac{dg}{dx}= frac{d(g)}{dx}+ frac{d(f)}{dx} )
C. ( frac{d(fg)}{dx}=f frac{d(g)}{dx}*g frac{d(f)}{dx} )
D. ( frac{d(fg)}{dx}=f frac{d(g)}{dx}+g frac{d(f)}{dx} )
Answer» E.
Discussion
5.

Power Rule of the derivative states that, ( frac{d(x^n)}{dx}=nx^{n-1}. )

A. True
B. False
Answer» C.
Discussion
6.

What is the maximum area of the rectangle with perimeter 620 mm?

A. 24,025 mm<sup>2</sup>
B. 22,725 mm<sup>2</sup>
C. 24,000 mm<sup>2</sup>
D. 24,075 mm<sup>2</sup>
Answer» B. 22,725 mm<sup>2</sup>
Discussion