Consider the following integral: dx I = Vx - x² a. Use the substitution u = x - ; to show that I = sin-(2x – 1) + C b. Use the substitution u = Vx to show that I = 2 sin-'(Vx) + C c. Show that IT 2 sin-(Vx) – sin-'(2x – 1) = 2.

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A: NOTE: Refresh your page if you can't see any equations. . the first function is 

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A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly re...

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A:

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A: Follow the procedure given. 

Q: Get the derivative of dz/dx. XY z =

A: Here we will find the derivative dz/dx,

Q: u - 1 Find dy/dx, given y : and u =Vx + 2. u* + 1

A: We can find the derivative as below.

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A: the given integral,     ∫t dtt4+64

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A:

Q: Discuss the similarities and differences between what it means for a sequence to converge and what i...

A: Let's find. 

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A: Let's find. 

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A: Solution of the problem as follows

Q: Let g(x, y) = cos(x + 2y). a. Evaluate g(2,–1). b. Find the domain of g. c. Find the range of g.

A: The function,      g(x,y)=cosx+2y

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A: We can solve the limit as below 

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A:

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Q: Write the first five terms of the sequence: 17 ln n n Determine whether the sequence converges, and ...

A: We will find the first five term of the sequence and also find the limit if given sequence is conver...

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A:

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A: If there is a sharp point at x=a on the graph , then function is not differentiable at x=a. If funct...

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A:

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A:

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A:

Q: EVALUATE AND SOLVE THE LINEAR DIFFERE NTI AL EQUAT O (05 - 150° + 10b* + GOD -72) y 2 12

A:

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A: We have too find direction derivative.

Q: dw for w = dt xez,x = t2,y = 1– t,z = 1+ 2t. e the Chain Rule to find

A: Given query is to find the derivative using chain rule.

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A: We have to find the value of x' at point (-2, -6) 

Q: Given that f(−5)=−10 and f′(−5)=−2, find an equation for the tangent line to the graph of y=f(x)at x...

A: Topic = Functions

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A: Explained below 

Q: 6. f(x) = 3sin (x +) + 1 Transformation: Domain: Range:

A:

Q: 21. 22. (D' + D - 9D' – 13D² + 8D + 12)y 0. Ans. y Ce+cze

A: We will solve the given differential equation.Below find the solution in the image.

Q: The following statement is TRUE except A. Derivative is the same as slope. B. A function is continuo...

A:

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Series  convergence and divergence 

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A:

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A: Given that: limx→0tan32xx3

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A:

Q: differential

A:

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A: We have to find tangent line

Q: 5. f(x) = In(x + 5) – 2 Domain: Range: Equation of Asymptote: End Behavior: lim f(x)= x→-5* lim f(x)...

A: Given : f(x) = ln(x+5) -2 To find : Domain, Range, Equation of Asymptote, and End behavior. 

Q: (х + 3)2 dx. J V40 – 6x - x²

A: Evaluate ∫x+3240-6x-x2dx=?

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818...

A: Let x=0.904818181818... Multiply 1000 on both sides.

Q: Solve the limit using table of values.

A: Given that: r(x)=x-2x+5,               x≤-44,                       -4&lt;x&lt;0x2-7x+4,          0≤...

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A:

Q: Differential Calculus:

A:

Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

A:

Q: Evaluate the integral. Show all your work. sin? x cos' xdx

A: ∫ sin2xcos3xdx

Q: Evaluate the limit (inx)" 10 lim x+5+(In 31x+10+(Inx) ×つ

A:

Q: 16 8 (B) y = - (x - 2) (C) y = } - }(2 – 2) (D) y = - ( – 2) %3D 3 %3D 16 (E) v=-유(z-2) 3 O.50

A:

Q: 2. lim 2. lim f(x) = 1 and f(0) = -3 1. lim f(x) = -1 and f(1)DNE x-1

A: 1. limx→1f(x)=-1 and f(1) DNE2. limx→0f(x)=1 and f(0)=-3

Q: Let f(x) = x' cos ( x-) and calculate ed S(x) dx by using integration by substitution. What was your...

A: