Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7

Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 7 Limits Ex 7.7 Questions and Answers.

Maharashtra State Board 11th Maths Solutions Chapter 7 Limits Ex 7.7

I. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow \infty}\left[\frac{a x^{3}+b x^{2}+c x+d}{e x^{3}+f x^{2}+g x+h}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 I Q1

Question 2.
\(\lim _{x \rightarrow \infty}\left[\frac{x^{3}+3 x+2}{(x+4)(x-6)(x-3)}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 I Q2

Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7

Question 3.
\(\lim _{x \rightarrow \infty}\left[\frac{7 x^{2}+5 x-3}{8 x^{2}-2 x+7}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 I Q3

II. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow \infty}\left[\frac{7 x^{2}+2 x-3}{\sqrt{x^{4}+x+2}}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q1
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q1.1

Question 2.
\(\lim _{x \rightarrow \infty}\left[\sqrt{x^{2}+4 x+16}-\sqrt{x^{2}+16}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q2
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q2.1

Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7

Question 3.
\(\lim _{x \rightarrow \infty}\left[\sqrt{x^{4}+4 x^{2}}-x^{2}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q3
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 II Q3.1

III. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow \infty}\left[\frac{\left(3 x^{2}+4\right)\left(4 x^{2}-6\right)\left(5 x^{2}+2\right)}{4 x^{6}+2 x^{4}-1}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q1
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q1.1

Question 2.
\(\lim _{x \rightarrow \infty}\left[\frac{(3 x-4)^{3}(4 x+3)^{4}}{(3 x+2)^{7}}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q2

Question 3.
\(\lim _{x \rightarrow \infty}[\sqrt{x}(\sqrt{x+1}-\sqrt{x})]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q3
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q3.1

Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7

Question 4.
\(\lim _{x \rightarrow \infty}\left[\frac{(2 x-1)^{20}(3 x-1)^{30}}{(2 x+1)^{50}}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q4

Question 5.
\(\lim _{x \rightarrow \infty}\left[\frac{\sqrt{x^{2}+5}-\sqrt{x^{2}-3}}{\sqrt{x^{2}+3}-\sqrt{x^{2}+1}}\right]\)
Solution:
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q5
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q5.1
Maharashtra Board 11th Maths Solutions Chapter 7 Limits Ex 7.7 III Q5.2