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

Maharashtra State Board 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2

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 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2

(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° = 0.0174c, √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° = 0.0175c, √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° = 0.0175c, √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° = 0.0175c.
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 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2

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) e0.995, 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 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2

(ii) e2.1, given that e2 = 7.389.
Solution:
Maharashtra Board 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2 Q4 (ii)

(iii) 32.01, 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) loge(101), given that loge10 = 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) loge(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) log10(1016), given that log10e = 0.4343.
Solution:
Maharashtra Board 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2 Q5 (iii)

Maharashtra Board 12th Maths Solutions Chapter 2 Applications of Derivatives Ex 2.2

Question 6.
Find the approximate values of:
(i) f(x) = x3 – 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) = x3 + 5x2 – 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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