Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 7 Limits Ex 7.5 Questions and Answers.

## Maharashtra State Board 11th Maths Solutions Chapter 7 Limits Ex 7.5

I. Evaluate the following:

Question 1.
$$\lim _{x \rightarrow \frac{\pi}{2}}\left[\frac{cosec x-1}{\left(\frac{\pi}{2}-x\right)^{2}}\right]$$
Solution:

Question 2.
$$\lim _{x \rightarrow a} \frac{\sin x-\sin a}{\sqrt[5]{x}-\sqrt[5]{a}}$$
Solution:

Question 3.
$$\lim _{x \rightarrow \pi}\left[\frac{\sqrt{5+\cos x}-2}{(\pi-x)^{2}}\right]$$
Solution:

Question 4.
$$\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{\cos x-\sqrt{3} \sin x}{\pi-6 x}\right]$$
Solution:

Question 5.
$$\lim _{x \rightarrow 1}\left[\frac{1-x^{2}}{\sin \pi x}\right]$$
Solution:

II. Evaluate the following:

Question 1.
$$\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{2 \sin x-1}{\pi-6 x}\right]$$
Solution:

Question 2.
$$\lim _{x \rightarrow \frac{\pi}{4}}\left[\frac{\sqrt{2}-\cos x-\sin x}{(4 x-\pi)^{2}}\right]$$
Solution:

Question 3.
$$\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{2-\sqrt{3} \cos x-\sin x}{(6 x-\pi)^{2}}\right]$$
Solution:

Question 4.
$$\lim _{x \rightarrow a}\left[\frac{\sin (\sqrt{x})-\sin (\sqrt{a})}{x-a}\right]$$
Solution:

Question 5.
$$\lim _{x \rightarrow \frac{\pi}{2}}\left[\frac{\cos 3 x+3 \cos x}{(2 x-\pi)^{3}}\right]$$
Solution: