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# matrices and calculus presentation.pptx

matrices

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### matrices and calculus presentation.pptx

1. 1. Matrices and calculus MA3151 TAYLOR’S SERIES By Syed Mohammed Aslam – 110122106033 Syed Mohammed Faheem – 110122106034 Vikram – 110122106035 Rithika – 110122106028
2. 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. 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. 4. f(6) (x) = -cos x ⇒ f(6)(0) = -1 Therefore, according to the Taylor series expansion; +..
5. 5. THANK YOU