1.
Matrices and calculus
MA3151
TAYLOR’S SERIES
By
Syed Mohammed Aslam – 110122106033
Syed Mohammed Faheem – 110122106034
Vikram – 110122106035
Rithika – 110122106028

2.
1.Evaluate the Taylor Series for f ( x ) = x3 −
10x2 + 6 at x = 3.
Solution :
First, we will find the derivatives of the given function.
f(x) = x3 − 10x2 + 6
⇒ f(3) = -57 ⇒f'(x) = 3x2 − 20x
⇒ f’(3) = 33 ⇒f’’(x) = 6x – 20
⇒ f’’(3) = -2 ⇒f’’’(x) = 6
⇒ f’’’(3) = 6 ⇒ f’’’’(x) = 0

3.
Solution: We need to take the derivatives of the cos x and evaluate them at x = 0
f(x) = cos x ⇒ f(0) = 1
f’(x) = -sin x ⇒ f’(0) = 0
f’’(x) = -cos x ⇒ f’’(0) = -1
f’’’(x) = sin x ⇒ f’’’(0) = 0
f’’’’(x) = cos x ⇒ f’’’’(4) = 1
f(5)(x) = -sin x ⇒ f(5) (0) = 0
• 2. Evaluate the Taylor Series for f ( x ) = cos ( x ) for x = 0

4.
f(6) (x) = -cos x ⇒ f(6)(0) = -1
Therefore, according to the Taylor series expansion;
+..

5.
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