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

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Question 1.

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.

(i) \(\frac{1}{5+x}\)

Answer:

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

Answer:

(iii) (5 + x^{2})^{2/3}

Answer:

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

Answer:

Question 2.

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

Answer:

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.

Answer:

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.

Answer:

Question 5.

Write the first 6 terms of the exponential series

(i) e^{5x}

Answer:

(ii) e^{-2x}

Answer:

(iii) e^{x/2}

Answer:

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.

Answer:

(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.

Answer:

Question 8.

Answer:

Question 9.

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

Answer:

Question 10.

Find the value of

Answer: