Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c)

Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions Inter 2nd Year Maths 2A Binomial Theorem Solutions Exercise 6(c) will help students to clear their doubts quickly.

Intermediate 2nd Year Maths 2A Binomial Theorem Solutions Exercise 6(c)

Question 1.
Find an approximate value of the following corrected to 4 decimal places.
(i) \(\sqrt[5]{242}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(i)

(ii) \(\sqrt[7]{127}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(ii)

(iii) \(\sqrt[5]{32.16}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(iii)

(iv) \(\sqrt{199}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(iv)

Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c)

(v) \(\sqrt[3]{1002}-\sqrt[3]{998}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(v)

(vi) \((1.02)^{3 / 2}-(0.98)^{3 / 2}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q1(vi)

Question 2.
If |x| is so small that x2 and higher powers of x may be neglected then find the approximate values of the following.
(i) \(\frac{(4+3 x)^{1 / 2}}{(3-2 x)^2}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(i)

(ii) \(\frac{\left(1-\frac{2 x}{3}\right)^{3 / 2}(32+5 x)^{1 / 5}}{(3-x)^3}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(ii)
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(ii).1

(iii) \(\sqrt{4-x}\left(3-\frac{x}{2}\right)^{-1}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(iii)

(iv) \(\frac{\sqrt{4+x}+\sqrt[3]{8+x}}{(1+2 x)+(1-2 x)^{-1 / 3}}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(iv)
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(iv).1

Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c)

(v) \(\frac{(8+3 x)^{2 / 3}}{(2+3 x) \sqrt{4-5 x}}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(v)
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q2(v).1

Question 3.
Suppose s and t are positive and t is very small when compared to s. Then find an approximate value of \(\left(\frac{s}{s+t}\right)^{1 / 3}-\left(\frac{s}{s-t}\right)^{1 / 3}\)
Solution:
Since t is very small when compared with s, \(\frac{t}{s}\) is very very small.
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q3

Question 4.
Suppose p, q are positive and p is very small when compared to q. Then find an approximate value of \(\left(\frac{q}{q+p}\right)^{1 / 2}+\left(\frac{q}{q-p}\right)^{1 / 2}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q4
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q4.1

Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c)

Question 5.
By neglecting x4 and higher powers of x, find an approximate value of \(\sqrt[3]{x^2+64}-\sqrt[3]{x^2+27}\)
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q5

Question 6.
Expand 3√3 in increasing powers of \(\frac{2}{3}\).
Solution:
Inter 2nd Year Maths 2A Binomial Theorem Solutions Ex 6(c) Q6