Given (a) (b) [³F(x) dx evaluate each definite integral. f(x) dx = 8 and f(x) dx = [ r3 6 nd [*1(x) dx = -7 [²F(x) dx = [ 6

Q: (a) [ dx ? 元+1

A:

Q: and g( x) = 7 − ( x − 3)^2 , a.) Solve for x: f ( x) = g( x) (Answers c

A: Inequality: a)f(x)=3x3-4x-3g(x)=7-(x-3)2f(x)=g(x)3x3-4x-3=7-(x-3)23x3+x2-10x-1=0The solution isx≈…

Q: fx₁y (x, y) = (a) To find 1 = → 1 = .. √ftcore cé {ere the ce e -J 1 = √ (c=³² [e¹ J² Jáx 2 = & [ -…

A: fx, yx, y=ce-xe-y, 0≤y≤x≤∞0, elsewhere We have to write text into digital format.

Q: flx)=x =X-5 (x)= Find .f)

A: Here, the given function is: f(x)=x-5, g(x)=x2

Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: Evaluate d/dx { In√(x+1)}

A:

Q: 2. (a) Evaluate [ x* V1+4x² dx. (b) Evaluate 8x° +13x dx. (x² +2)²

A: (a) We have to evaluate the following integral: ∫01x21+4x2dx Then we get,…

Q: Inx (a) log₂x = In2 (b) dx =

A: We have to prove that: (a) log2x=lnxln2 (b) ddxtan-1x=11+x2

Q: -1)/(x4))1/2

A:

Q: d Use the Product Rule to find the derivative [(x + 3)(3x + 8)]. dx Answer

A: Explanation of the answer is as follows