SOLVE NUMERICALLY USING (a) TRAPEZOIDAL RULE AND (b) SIMPSON RULE. USE (a) n = 4, and (b) n = 8. COMPARE THEM WITH THE RESULT WHEN SOLVED ANALYTICALLY.

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A: Topic:- application of derivatives and integration

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A: Topic:-  limit and continuity

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A: Topic:- derivatives

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A: To find the distance from the point to the line.

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A: This question can be solved using the concept of natural logarithm.

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A: Linear approximation for fx=x at a=25The linear approximation of the function fx at point a is Lx =…

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A: Please refer to the image below

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A: Topic:- application of derivatives

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A: ∑k=1∞ 1k+3-1k+4

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A: For critical points , f'(x) =0.

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A: Concept: Derivative of log(x) is  logx' logx'=1xln(10)....................(as log is default base…

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Q: .

A: Please refer to the image below

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A: The given problem is solved below in detail.

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A: Let's solve given integration by using simpson 1/3 method.

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A: The given problem is solved below in detail.