Evaluate the integral 24 2 (2³7) dz by making the substitution u = x5 - 7. > Next Question + C NOTE: Your answer should be in terms of x and not u.

Q: Consider the function below. f(x) = x²e-x (a) Find the exact value of the minimum of f for x ≥ 0.…

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Q: 9 Write the Taylor Series for f(x) = sin(x) at x = 12/12/2 as & Cn (x-7) n Find the first 5…

A: Taylor serues

Q: The rational function 310t V(t)= t + 2 models the velocity, V(t), in miles per hour, of a dragster t…

A: The rational function is given as  V(t)=310tt+2 The changed function of the velocity is…

Q: Evaluate the integral by making the appropriate substitution: u = f2¹ (25 - 4) 43³dz = dx 43 fz¹ª…

A: To evaluate the integral.

Q: Convert the equation r= -14 sin 0 to Cartesian coordinates. Describe the resulting curve. Choose the…

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Q: 8 W n=1 Determine whether the following series converge absolutely, converge conditionally, or…

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Q: If J ㅠ O OT 2 O F/4 π 5100 3 dx x² - G(x) + C, what is G(1) - G(0)?

A: To find integration of given function.

Q: The masses m; are located at the points P₁. Find the moments Mx and My and the center of mass of the…

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Q: 5x (d) . x²-x-6 dx

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Q: #1₁ S (3) Find d dt 1+ t²

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Q: If ? what is f(x) = ex -1 f-¹ (x)

A: We  are asked to find inverse of the function

Q: What is the standard form equation of an ellipse that has vertices (-4,-13) and (-4, 11) and…

A: What is the standard form equation of an ellipse that has vertices (-4, -13) and (-4, 11) and…

Q: Find the following using the table below. x 1 2 3 4 f(x) 2 1 4 f'(x) 3 1 g(x) 4 3 2 1 g'(x) 1 3 2 4…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. rsin 0=6 The…

A: in cartesian  coordinates  x=rcosθ  and  y=rsinθgiven  rsinθ=6

Q: 7. Find the area of the portion of the plane that is inside the triangle with vertices (0,0,4), (8,…

A: See this solution in below.

Q: Graphs of implicit equations between and True X do not necessarily represent functions. O False Y

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Q: O Find the area of the region bounded by y = 4x - x² and y = x² - 2x.

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Q: The formula V = kr4 is used to predict how much the radius of a partially clogged artery has to be…

A: Given V = kr4where V = volume of fluid flow k = constant r = radius

Q: Which means the same as arctanx

A: Given, Which means the same as arctan(x)

Q: weekly number of pounds of acetate fibers that can be produced is given by the function: z = f(x, y)…

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Q: Let g(x) = *F(t) dt, where f is the function whose graph is shown. YA 1 0 3 f 6 9 t O A. Find g(3)…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: To find the equation of tangent to the given curve.

Q: Which of the following is the linear approximation of f(x) = sin x at x = ? OL(x) 1 OL(x) = x OL(x)…

A: Given f( x )= sinx at x = π2linear approximation L( x ) = f( a ) + ( x - a )f'( a )

Q: Textbook D Videos [+] Set up the definite integral required to find the area of the region between…

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Q: If f(x) = x² and g(x) = 0 (6³-a³) O None of these. O2(6²-a²) 026-2a 06² q² what is g(x)da?

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Q: O Find the points at which the polar curve r = 4cose has horizontal tangent lines.

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Q: List each of the mistakes in the following calculations: d a) [(cos z)] = x(cos x)²-1 da d b) [(cos…

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Q: whose center is located at the x axis? a) (x² + y²)dr + 2xydy=0 e) (2²-y)dz +2rydy=0

A: we have to find the differential equation of the family of circles that passes through the origin…

Q: x = The position of an object at time t is given by the parametric equations y = 5t² + 1 Find the…

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Q: 27) Suppose y = f(x) and y = g(x) are continuous functions which intersect at x = 1, x = 4 and x = 7…

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Q: For the function f(x) = 5x - 5x, evaluate and simplify. f(x +h)-f(x) h

A: Given query is to perform indicated operation m

Q: 7 Suppose f(x) dx = 6 and Then 5 12 S™ f(x) dx 5 12 of,"s 7 = f(x) dx = 5.

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Q: Consider the following function: Step 4 of 4: Enter the x-values of any local minima, maxima, and…

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Q: If f(x) = In x where x > 0, what is In r 2 1 2√ ln x O 1 2x ln x 1 2x 1 d (f (√)). ? dx

A: Given: fx=lnx To find: dfxdx Now, first we need to find fx fx=lnx ⇒fx=lnxy2 ⇒fx=12lnx

Q: The weight of a body, W, above the surface of the Earth varies inversely with the square of the…

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Q: the demand for a product is $14 and the total costs are C(x)=0.2x2+6.4x+2. What is the maximum value…

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Q: Match the following functions with the general shape of their graphs. Functions f(x) = ln (x + 2) -…

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Q: Let C be the curve f(x) = the length of C, as follows: In(x) X 2 4 - between x = 1 and x = e.…

A: Arc length

Q: Given the ellipse below, determine the coordinates of the two foci. Enter the coordinates as ordered…

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Q: 18) Determine the annihilator of y-z-efsinz. a) (D-2D³-2D²)y=0 b) (D+2D³ +2D²)y=0 e) (D¹+2D³-2D)v-0…

A: The given equation is; y=x-exsinx.

Q: Write the standard form equation of a hyperbola that has vertices (±7,0) and foci (±√53,0). Provide…

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Q: Find the linear approximation to the equation f(x, y) approximate f(6.28, 4.16). f(6.28, 4.16) xy at…

A: Given  fx,y=5xy6 The objective is to find the linear approximation to the equation.

Q: Question 8 Consider the indefinite integral U= du = x5 (x6 + 4)6 This can be transformed into a…

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Q: Assume f and g are inverse functions. Which of the following statements is/are true? 1. y = f(x) if…

A: Please see the below picture for detailed solution.

Q: The cost C'(x), where is the number of miles driven, of renting a car for a day is $48 plus $0.95…

A: Let's find linear function.

Q: Graph the circle given below by moving the key points: To graph the circle, drag the center point to…

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Q: What is d dx 7x 3x O 102 sin z √2 - sint dt? O-3√2-Sin 3z - 7√2 – sin 77 O 3√2-sin 3x - 7V2 — sin 72…

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Q: 1 3 2 1 q To find the blue shaded area above, we would calculate: b [* f(x)dx = area Where: a = f(x)…

A: Please see the below picture for detailed solution.

Q: 1. Evaluate the indefinite integral f sinecose de 1+sin²0

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Q: 2 4/1 1 (3) Find d dt 1 + t2

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