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:

(ii) \(\sqrt[7]{127}\)
Solution:

(iii) \(\sqrt[5]{32.16}\)
Solution:

(iv) \(\sqrt{199}\)
Solution:

(v) \(\sqrt[3]{1002}-\sqrt[3]{998}\)
Solution:

(vi) \((1.02)^{3 / 2}-(0.98)^{3 / 2}\)
Solution:

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:

(ii) \(\frac{\left(1-\frac{2 x}{3}\right)^{3 / 2}(32+5 x)^{1 / 5}}{(3-x)^3}\)
Solution:

(iii) \(\sqrt{4-x}\left(3-\frac{x}{2}\right)^{-1}\)
Solution:

(iv) \(\frac{\sqrt{4+x}+\sqrt[3]{8+x}}{(1+2 x)+(1-2 x)^{-1 / 3}}\)
Solution:

(v) \(\frac{(8+3 x)^{2 / 3}}{(2+3 x) \sqrt{4-5 x}}\)
Solution:

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.

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:

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:

Question 6.
Expand 3√3 in increasing powers of \(\frac{2}{3}\).
Solution: