Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 7 Limits Ex 7.4 Questions and Answers.

## Maharashtra State Board 11th Maths Solutions Chapter 7 Limits Ex 7.4

I. Evaluate the following limits:

Question 1.

\(\lim _{\theta \rightarrow 0}\left[\frac{\sin (m \theta)}{\tan (n \theta)}\right]\)

Solution:

Question 2.

\(\lim _{\theta \rightarrow 0}\left[\frac{1-\cos 2 \theta}{\theta^{2}}\right]\)

Solution:

Question 3.

\(\lim _{x \rightarrow 0}\left[\frac{x \cdot \tan x}{1-\cos x}\right]\)

Solution:

Question 4.

\(\lim _{x \rightarrow 0}\left(\frac{\sec x-1}{x^{2}}\right)\)

Solution:

II. Evaluate the following limits:

Question 1.

\(\lim _{x \rightarrow 0}\left[\frac{1-\cos (n x)}{1-\cos (m x)}\right]\)

Solution:

Question 2.

\(\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{2-{cosec} x}{\cot ^{2} x-3}\right]\)

Solution:

Question 3.

\(\lim _{x \rightarrow \frac{\pi}{4}}\left[\frac{\cos x-\sin x}{\cos 2 x}\right]\)

Solution:

III. Evaluate the following limits:

Question 1.

\(\lim _{x \rightarrow 0}\left[\frac{\cos (a x)-\cos (b x)}{\cos (c x)-1}\right]\)

Solution:

Question 2.

\(\lim _{x \rightarrow \pi}\left[\frac{\sqrt{1-\cos x}-\sqrt{2}}{\sin ^{2} x}\right]\)

Solution:

Question 3.

\(\lim _{x \rightarrow \frac{\pi}{4}}\left[\frac{\tan ^{2} x-\cot ^{2} x}{\sec x-{cosec} x}\right]\)

Solution:

Question 4.

\(\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}\right]\)

Solution: