Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) [(x3/2. x3/2 + 10x + 4) dx -4) c

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Q: 8) Prove sin (x+y) sin (x-y) = tan(x)+tan (y) tan(x)-tan (y)

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Q: (a) In(a + b) In(a)In(b) for all a,b > 0 OTrue False (b) In(a-b) In(a) + In(b) for all a,b>0 OTrue…

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A: Solve

Q: Show that the equation x3 - 15x + c = 0 has at most one solution in the interval [-2, 2].

A: The given equation is; x3 - 15x + c = 0

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Q: 1. Suppose f is differentiable everywhere, f(0) = -1/2, and f' is graphed below. 2- (a) Find all…

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Q: Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).

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Q: -15 4 -3 गी 9 6 2 6 $ ई 4 s े + + ई 4 -$ + -7 2

A: Here we have graph of a function f(x)  Then we have to write it's domain

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A: I am attaching image so that you understand each and every step.

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Q: Find the limit. 7 lim (1 + 2x)2 Inx X-8 7 = lim (1+2x)2 Inx | (Type an exact answer X→∞

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Q: Find the arc length of y= 2x sqrt(x), from x=0 to x=1

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Q: 13. After t weeks of practice, a typing student can type w(t) 100(1e-0.4t) words per minute. How…

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Q: Find the exact length of the curve. y 1/4x² - 11/12 In(x), = -X 1 ≤ x ≤ 4

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Q: 6) Prove cos4x -sin+x= cos 2x

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Q: For the given cost function C(x) = 12100 + 200x + x² find: a) The cost at the production level 1100…

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Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: 16+² x da

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A: Please see the below picture for detailed solution.

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation r(t) =…

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Q: 4 [ (2x³ + 5x) dx with n −1 = 10 steps

A: Given question:- Find an upper bound for ET in estimating A 5 B 5/4 C 10 D 64/25

Q: dy For the equation, use implicit differentiation to find dx y5 - x² = 6

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Q: Match the vector field with its graph. F(x,y) - d + 30 트 토 ++ 11/

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Q: 2 Let f(x) = √3x² + 3x + 2 f'(x) = ƒ'(1): = OF

A: Topic - Derivative of  a function We are given, f(x)=3x2+3x+2Formulas usedChain rule:…

Q: Solve the corresponding differential equation given the general solution via elimination of…

A: We can find the differential equation of the given curve by eliminating the arbitrary constant a.