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Problem Questions with Answer, Solution - Exercise 7.4 : Series Expansions: Maclaurin’s and Taylor’s Series | 12th Maths : UNIT 7 : Applications of Differential Calculus

Chapter: 12th Maths : UNIT 7 : Applications of Differential Calculus

Exercise 7.4 : Series Expansions: Maclaurin’s and Taylor’s Series

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EXERCISE 7.4

1. Write the Maclaurin series expansion of the following functions:

(i) ex

(ii) sin x

(iii) cos x

(iv) log(1- x) ; –1 ≤ x < 1

(v) tan-1 (x) ; –1 ≤ x ≤ 1

(vi) cos2 x




2. Write down the Taylor series expansion, of the function log x about x = 1 upto three non-zero terms for x > 0.


3. Expand sin x in ascending powers x  π/4 upto three non-zero terms.


4. Expand the polynomial f (x) = x2 – 3x + 2 in powers of x – 1.


Answers:


(4) f (x) = − ( x −1) + ( x −1)2

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12th Maths : UNIT 7 : Applications of Differential Calculus : Exercise 7.4 : Series Expansions: Maclaurin’s and Taylor’s Series | Problem Questions with Answer, Solution

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12th Maths : UNIT 7 : Applications of Differential Calculus


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