Balbharti 12th Maharashtra State Board Maths Solutions Book

Pdf Chapter 2 Applications of Derivatives Ex 2.2 Questions and Answers.

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 e² = 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_e10 = 2.3026.
Solution:



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



(iii) log₁₀(1016), given that log₁₀e = 0.4343.
Solution:




Question 6.
Find the approximate values of:
(i) f(x) = x³ – 3x + 5 at x = 1.99
Solution:



(ii) f(x) = x³ + 5x² – 7x +10 at x = 1.12
Solution: