Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 7 Limits Ex 7.1 Questions and Answers.

## Maharashtra State Board 11th Commerce Maths Solutions Chapter 7 Limits Ex 7.1

I. Evaluate the following limits:

Question 1.
$$\lim _{x \rightarrow 3}\left[\frac{\sqrt{x+6}}{x}\right]$$
Solution:

Question 2.
$$\lim _{x \rightarrow 2}\left[\frac{x^{-3}-2^{-3}}{x-2}\right]$$
Solution:

Question 3.
$$\lim _{x \rightarrow 5}\left[\frac{x^{3}-125}{x^{5}-3125}\right]$$
Solution:

Question 4.
If $$\lim _{x \rightarrow 1}\left[\frac{x^{4}-1}{x-1}\right]=\lim _{x \rightarrow a}\left[\frac{x^{3}-a^{3}}{x-a}\right]$$, find all possible values of a.
Solution:

II. Evaluate the following limits:

Question 1.
$$\lim _{x \rightarrow 7}\left[\frac{(\sqrt[3]{x}-\sqrt[3]{7})(\sqrt[3]{x}+\sqrt[3]{7})}{x-7}\right]$$
Solution:

Question 2.
If $$\lim _{x \rightarrow 5}\left[\frac{x^{k}-5^{k}}{x-5}\right]=500$$, find all possible values of k.
Solution:

Question 3.
$$\lim _{x \rightarrow 0}\left[\frac{(1-x)^{8}-1}{(1-x)^{2}-1}\right]$$
Solution:

III. Evaluate the following limits:

Question 1.
$$\lim _{x \rightarrow 0}\left[\frac{\sqrt[3]{1+x}-\sqrt{1+x}}{x}\right]$$
Solution:

Question 2.
$$\lim _{y \rightarrow 1}\left[\frac{2 y-2}{\sqrt[3]{7+y}-2}\right]$$
Solution:

Question 3.
$$\lim _{z \rightarrow a}\left[\frac{(z+2)^{\frac{3}{2}}-(a+2)^{\frac{3}{2}}}{z-a}\right]$$
Solution:

Question 4.
$$\lim _{x \rightarrow 5}\left[\frac{x^{3}-125}{x^{2}-25}\right]$$
Solution: