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:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-i
√8.95 = 2.9917

(ii) \(\sqrt[3]{28}\)
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-ii

(iii) \(\sqrt[5]{31.98}\)
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-iii

Maharashtra-Board-Solutions

(iv) (3.97) 4
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-iv
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-iv.1

(v) (4.01) 3
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q1-v

Question 2.
Find the approximate values of:
(i) sin 61°, given that 1° = 0.0174 c , √3 = 1.732.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-i

(ii) sin(29° 30′), given that 1° = 0.0175 c , √3 = 1.732.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-ii
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-ii.1

(iii) cos(60° 30′), given that 1° = 0.0175 c , √3 = 1.732.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-iii

(iv) tan (45° 40′), given that 1° = 0.0175 c .
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-iv
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q2-iv.1

Maharashtra-Board-Solutions

Question 3.
Find the approximate values of
(i) tan -1 (0.999).
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q3-i

(ii) cot -1 (0.999).
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q3-ii
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q3-ii.1

(iii) tan -1 (1.001).
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q3-iii

Question 4.
Find the approximate values of:
(i) e 0.995 , given that e = 2.7183.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q4-i
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q4-i.1

Maharashtra-Board-Solutions

(ii) e 2.1 , given that e 2 = 7.389.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q4-ii

(iii) 3 2.01 , given that log 3 = 1.0986.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q4-iii

Question 5.
Find the approximate values of:
(i) log e (101), given that log e 10 = 2.3026.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q5-i
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q5-i.1

(ii) log e (9.01), given that log 3 = 1.0986.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q5-ii
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q5-ii.1

(iii) log 10 (1016), given that log 10 e = 0.4343.
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q5-iii

Maharashtra-Board-Solutions

Question 6.
Find the approximate values of:
(i) f(x) = x 3 – 3x + 5 at x = 1.99
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q6-i
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q6-i.1

(ii) f(x) = x 3 + 5x 2 – 7x +10 at x = 1.12
Solution:
Maharashtra-Board-12th-Maths-Solutions-Chapter-2-Applications-of-Derivatives-Ex-2.2-Q6-ii

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