Evaluate using Integration by Parts, substitution, or both if necessary. (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) 7x dx V7x + 1

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A: Given query is to find the function f(O).

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A: Topic = Trigonometry

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A: sinh x1+cosh x

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A: ∫ ex dx = ex +C

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A: scalar projection of w on v is =v.w|v||w|compvw¯=…

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A: Using the alternating series reminder theoram to find the number of terms.

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A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

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A: We will answer only part c, d and e because you have mentioned to solve only these three.   Complete…

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A: Answer is in below step.

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A: f(x)=-3x4+12x+2f'(x)=-12x2+12f'(x)=0-12x2+12=012x2=12x2=1x=±1Critical points ;…

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A: This question is based on substitution of given integral.

Q: Exercise To Try 7 Let f(x) = V. Estimate the area A under the graph y = Va between a = 1 and b= 4…

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A: The given question can  be solved as shown in step2.

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Q: 10. dx 1+cos 3x In(1+cos 3x) + C %3D - 3 _11. S 2(cos x)(sin²x)dx 2 + C 3

A: As you mentioned  only 10 &amp; 11 solved

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A: Solving

Q: In Problems 25-32, find the indicated value. 25. f.(1,3) if f(x, y) = 5x'y- 4xy2

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Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) 12 dt 3t +4

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