Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4

Question 1.
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
(i) $$\frac{1}{5+x}$$

(ii) $$\frac{2}{(3+4 x)^{2}}$$

(iii) (5 + x2)2/3

(iv) $$(x+2)^{-\frac{2}{3}}$$

Question 2.
Find $$\sqrt[3]{1001}$$ approximately. (two decimal places)

Question 3.
Prove that $$\sqrt[3]{x^{3}+6}-\sqrt[3]{x^{3}+3}$$ is approximately equal to $$\frac{1}{x^{2}}$$ when x is sufficiently large.

Question 4.
Prove that $$\sqrt{\frac{1-x}{1+x}}$$ is approximately equal to 1 – x + $$\frac{x^{2}}{2}$$ when x is very small.

Question 5.
Write the first 6 terms of the exponential series
(i) e5x

(ii) e-2x

(iii) ex/2

Question 6.
Write the first 4 terms of the logarithmic series.
(i) log (1 + 4x)
(ii) log (1 – 2x)
(iii) log $$\left(\frac{1+3 x}{1-3 x}\right)$$
(iv) log $$\left(\frac{1-2 x}{1+2 x}\right)$$
Find the intervals on which the expansions are valid.
(i) log ( 1 + 4x )

(ii) log (1 – 2x)

(iii) log $$\left(\frac{1+3 x}{1-3 x}\right)$$

(iv) log $$\left(\frac{1-2 x}{1+2 x}\right)$$

Question 7.

Question 8.

Find the coefficient of x4 in the expansion of $$\frac{3-4 x+x^{2}}{e^{2 x}}$$