Applications of Derivatives Class 12 Maths 2 Exercise 2.2 Solutions Maharashtra Board

Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 2 Applications of Derivatives Ex 2.2 Questions and Answers.

12th Maths Part 2 Applications of Derivatives Exercise 2.2 Questions And Answers Maharashtra Board

Question 1.
Find the approximate value of given functions, at required points.
(i) √8.95
Solution:

√8.95 = 2.9917

(ii) \(\sqrt[3]{28}\)
Solution:

(iii) \(\sqrt[5]{31.98}\)
Solution:

(iv) (3.97) ⁴
Solution:

(v) (4.01) ³
Solution:

Question 2.
Find the approximate values of:
(i) sin 61°, given that 1° = 0.0174 ^c , √3 = 1.732.
Solution:

(ii) sin(29° 30′), given that 1° = 0.0175 ^c , √3 = 1.732.
Solution:

(iii) cos(60° 30′), given that 1° = 0.0175 ^c , √3 = 1.732.
Solution:

(iv) tan (45° 40′), given that 1° = 0.0175 ^c .
Solution:

Question 3.
Find the approximate values of
(i) tan ^-1 (0.999).
Solution:

(ii) cot ^-1 (0.999).
Solution:

(iii) tan ^-1 (1.001).
Solution:

Question 4.
Find the approximate values of:
(i) e ^0.995 , given that e = 2.7183.
Solution:

(ii) e ^2.1 , given that e ² = 7.389.
Solution:

(iii) 3 ^2.01 , given that log 3 = 1.0986.
Solution:

Question 5.
Find the approximate values of:
(i) log _e (101), given that log _e 10 = 2.3026.
Solution:

(ii) log _e (9.01), given that log 3 = 1.0986.
Solution:

(iii) log ₁₀ (1016), given that log ₁₀ e = 0.4343.
Solution:

Question 6.
Find the approximate values of:
(i) f(x) = x ³ – 3x + 5 at x = 1.99
Solution:

(ii) f(x) = x ³ + 5x ² – 7x +10 at x = 1.12
Solution: