Consider the vector-valued function R(t) = (t³ — t, 2t²,2 — 21.²). 1. Find ||'(t) || (Simplify your answer.) 2. Find the distance traveled by a particle moving along the curve from the point where t = -1 to the point where t = 2.

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A: Topic = Limits

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Q: Show

A: Please refer to the image below

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A: Here is the solution of the given problem.  To solve this problem we use simple concept of…

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A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

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A: ∫ 351x2-9dx

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A: topic- algebra

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A: We have to find polar form

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A:

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A: We have to find symbol of antidifferentiation.

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A: Given problem:- A rectangle is constructed with its base on the diameter of a semicircle with radius…

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A: In this question, we want to know whether the given statement is true or false.

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A: projectile motion

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A: Given that the sum of the digits of a 3-digit number is 11. If the digits are reversed the new…

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Q: Find the complete solution of e sinx- - Note: fe" du = e" + C dy cos² x=0. dx

A: e-y sin x-dydx cos2 x=0⇒dydx cos2 x=e-y sin x⇒ey dy=sin x cos2 x dx⇒ey dy=sin x cos x·1 cos x dx⇒ey…

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A: It will solve by part method integration  ∫u v dx = u∫v dx −∫u' (∫v dx) dx u is the function u(x) v…

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A: Option E is not correct .

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A: Given ∫012(x+2)2 dx To evaluate integral using Trapezoidal Rule:

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A: We find the line integral in the following way

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A: Link between line and plane.

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A: Given is       power series ∑n=0∞(-3)n(x-2)n(n+2)when x=53∑n=0∞(-3)n(x-2)n(n+2)=…

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A: We have to find the solution

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A: We have to find the solution

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A: Integration

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A: Please see the below picture for detailed solution.

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A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

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A: Solution is here

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A: First we evaluate f(x) using substitution

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A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

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A: As we know that; The trigonometric ratios;…

Q: (A) True B) False 3

A: