Evaluate the function at the given value of the independent variable. Simplify the results. f(x) = x³ f(x + Ax) = f(x) Δχ (Ax = 0) W5

Q: 2x log 2x dr 1 (x²+6x+5)3/2 dr

A: As we know that; The Power Rule: ∫xndx=xn+1n+1+C   1). The given integral is: I=∫2xlog2xdx Apply the…

Q: Which equation represents a line that goes through the points (0, 1) and (1, 0)? y = -(x + 1) y = 1…

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300…

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Q: Consider the region bounded by x=4-y, the y-axis and the x-axis. 1 2 3 4 The volume of the solid…

A: Given:-

Q: 1. Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The centroid of R is: a.…

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Q: Set up the triple integral in spherical coordinates that solves the volume of the solid bounded…

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Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: III. Consider a function f that is continuous everywhere except at x = 1. Given below is t table of…

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Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d dr 11 t²dt =

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Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: Define the force field F(x, y, z) = (xy, —-yz, xz). Find the divergence and curl of F. Let C be the…

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Q: Evaluate the following limit: √x-2 lim- x+4 T²-16 01 32 Oº O O undefined 032

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Q: Evaluate the following limits if they exist: lim In (3x-1) 5+x x->-5 e a) b) x-lnx lim x-e* lnx-1 El

A: limx→-5ln3x-1e5+x

Q: Find the total surface area and volume of the solid object shown to the right. Use the key for s The…

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Q: Given that answer = [*f(x) dx = 45 13 > [². what is f(v)dv?

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Q: O

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Q: Date 3. Determine if the equation is homogeneous in what degree then solve for the general /…

A: Solution

Q: -3x²+tan(3x-5) Explain the steps you would take to find the derivative of f(x) = (e

A: Our Aim is to find the derivative of f(x)=12e-3x2+tan3x-5 -(i)

Q: Evaluate the following antiderivative/indefinite integral: / [(5x² + ² + + 50² + 7) de 36 X x3 k:…

A: Topic:- application of integration

Q: 19. Which of the integrals below represents the set-up of ff xy dS, where S is th vertices (1, 0,…

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Q: let cosx=-4/5, pi<2<3pi/2. find csc(x/2).

A: Solved below

Q: 2 8 X2 x4 + x2 dx

A: To solve the given integral.

Q: This equation is an example of which one of the following? Ax + By > C A two-variable inequality…

A: Since , x and y are variables , therefore given inequality is a  Two - variable inequality. Option…

Q: Consider the integral (ln(x))6 dx:

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Q: S= [²3/1/20 The value of dr is

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Q: Consider the function f(x) = 2x + 6x510x² - 4. = Enter an antiderivative of f(x). Do not enter +c as…

A: Here we have to find the integration.

Q: Which of the following equations represent(s) a line that goes through the points (2,3) and (1,1)?…

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors 1² +2 x² +2…

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Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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Q: Below is the graph of y = x² +5. 401 D 30- 20 10- -3 -2 -1 0 1 2 3 4 5 6 The area bounded by y = x²…

A: the area bounded by the curve y=x^2 +5 and the x axis from x=2 to x=5

Q: Given f''(x) = 7x + 4 and f'(0) -2 and f(0) - 3.

A: Given that f"(x)=7x+4 and f'(0)=-2 and f(0)=-3Our Aim is to find f'(x) and f(4)=?

Q: A particle is moving with a position function given by s(t) = 6t² - in metres and time in seconds.…

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Q: Which of the following equations represents a line that passes through the point (0, 1) and has a…

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Q: 25. The vector field F(x, y, z) = (2xy + tan x)i + (x²-√y² - 1)j is conservative. a) True b) False

A: To determine whether the following statement is True or False.The vector field F→x, y, z=2xy+tan…

Q: -5 -5- 0 -5-

A: Topic- Inequalities

Q: If f(x) = 1 - log5 x, then f-¹(x) =

A: Given that f(x)=1-log5 x , then our aim is to find the value of f-1 (x)=?

Q: Gr 5 0 -5 5

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Q: IV. Fill in the blank to make each statement true. Use correct notations. 3. If a polynomial…

A: We can solve this as follows:

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

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Q: Solve the given initial value problem. y'' - 4y' + 3y = 0; The solution is y(t) = y(0) = - 1 2 y'(0)…

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Q: Given the function graphed below, evaluate the definite integrals. -1 4 3 2 1 1 -1 -2 -3 -4+ […

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Q: Provide the complete solution (typewritten if possible) for the item below. Consider the plane π…

A: The equation of the plane π is given as , x-2y+3z-1=0 and the line l is x=1-y2=z+1 Find the…

Q: The class outing ticket includes a snack-pack with three items, a cooldrink, chocolate and then…

A: Given tree diagram shows all the possible combination of "cooldrinks", "chocolates" and "chips or…

Q: IV. Fill in the blank to make each statement true. Use correct notations. 12π ¹ (sin ¹2) = 5 1. sin¹…

A: We can find the answer in the following steps.

Q: The critical numbers r = -1 and x = 2 are found from a continuous derivative f(x). Given that the…

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Q: The graph of a function is given. Determine the average rate of change of the function between the…

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Q: 2nx 5x e e dx

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Q: Which of the following graphs represents (x + 1)² = 8(y - 3)?

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Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. 3 + 6x3/2 f(x, y) R:…

A: In this question, we need to find the area of the surface.