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:

√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: