If f'(x) = 5x4, what is f(x)? (Remember the constant of integration.) f(x) =

Q: For Evaluate the following expression. Select the correct answer below: f(x) 4-x-x² ifxsl 2x-1 ifx>1…

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Q: The time it takes an object to hit the ground, if air resistance is ignored, is a function only of…

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Q: Region R is bounded by the graphs of y=e²x+1, y=0, x=0, and .x = 2, Which of the following integrals…

A: Region is bounded by y=e2x+1,y=0,x=0, and x=2Rotating the region about x-axisUsing the disk method

Q: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

A: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

Q: Given [f xydA where region R is the rectangle bounded by (0,0), (1,1), (2,0) and R (1,-1), use…

A: We have given the given integral is, where R is the parallelogram with vertices (0, 0),(1, 1),(2,…

Q: 1. [xds, where C is the curve y=x², z = 0 from (0, 0, 0) tom (1, 1,0)

A: 1.∫Cxds,where C is the curve y=x2,z=0 from (0,0,0) to (1,1,0)y=x2 from (0,0) to (1,1)Let…

Q: 10) Find the indicated limit 2x x+1 lim( x-x

A: (10) limx→∞(2xx2+1)

Q: Find the area under the given curve. y = √√x +6; from x=0 to x = 16

A: Consider the curve

Q: Find all of the real and imaginary zeros for the polynomial function. y=11x³-67x²+281x-25

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Q: Find a parametrization of the line in which the planes x+2y+4z=-4 and 2x+3y+6z= -7 intersect. Find…

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Q: Determine the relative extrema for the function: y=2xe^x Group of answer choices relative minimum…

A: The objective of this question is to find the relative extrema of the function y=2xe^x. Relative…

Q: Calculate af ax af af ax af Əy (1, -1) af af af af ax' ay ax (1, -1) ay (1,-1) f(x, y) = 7,000 - 65x…

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Q: Question Given the graph of f(x) below, Identify the graph of f'(x). Select the correct answer…

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Q: Let R be the region in the first quadrant bounded by the lines y = hyperbolas xy = 1, xy = 2. (a)…

A: Given that let R be the region in the first quadrant bounded by the lines  and  and the hyperbolas

Q: Select the graph for which f(x) > 0 and a) r f(x) < 0

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Q: Question 18 ▼ = Starting with an initial population of P(0) = 19, the population of a pride of…

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Q: Solve the initial value problem below using the method of Laplace transforms. ty'' - ty' + y = 5,…

A: The initial value problem is given as,solve the problem.

Q: Question Suppose K(x) = f(g(h(x))). Given the table of values below, determine k'(0). x f(x) g(x)…

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Q: Select the graph for which a) ƒ¹(x) > 0 and f11(x) > 0

A: It is given that, the f'(x)&gt;0 Which means the function f(x) is increasing.Therefore Graph-a is…

Q: If g(x)=-4) - 4x, then g '(x) is equal to which of the following? 2 X g'(x) = -x X O g'(x) = 1/2-4…

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Q: Problem #4: Consider SS (V x F) ndS S where F = 14ex²+y² i + 1le=³j + ln(z+2)x-cosy k and S is the…

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Q: 5. Use a triple integral to find the volume of the solid in the first octant bounded by the plane 2x…

A: Solid in the first octant bounded by the plane 2x+3y+6z=12 and the coordinate…

Q: Estimate the area under the graph of f(x) =3x² + 12x + 14 over the interval [0, 3] using five…

A: To estimate the area under the graph of  over the interval  by using five approximating…

Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = -0.003t² +0.2t, where…

A: Given that in a memory experiment the rate of memorizing is given by  ,where M'(t) is the memory…

Q: As with discrete-time dynamical systems, equilibria can act strange when the slope of the…

A: We have to graph a rate-of-change function that has a slope of 0 at the equilibrium but the…

Q: Find the volume of the region bounded by the planes 4x + 2y + 3z = 5, y = x, x = 0, z = 0.

A: 4x+2y+3z=5,y=x,x=0,z=0.0≤z≤(5−4x−2y)3z=0⇒y=5−4x2x≤y≤5−4x25−4x2=x5−4x=2xx=56

Q: Evaluate the definite integral a) Find an anti-derivative [2√ada 6 [2√æda 0 b) Evaluate 6 [2√ada = =…

A: To evaluate the following definite integral.

Q: Given that f₁ f(x) da = 7 and fº₁ƒ(x) dx = -2. dx fő 2f (x) dx. evaluate

A: ∫−15f(x)dx=7 and ∫−10f(x)dx=−2Using the definite integral property∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx

Q: Write an equation of the graph in the final position. The graph of y= 2* is shifted 4 units left and…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 4t, where 0 ≤ t ≤ 2.5…

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Q: Evaluate the following indefinite and definite integrals using substitution.  Show all work, thank…

A: use substitution method for solving such integral

Q: Let S be the solid that lies between the paraboloid z = x² + y² and the sphere x² + y² +z² = 2. (a)…

A: Given that  S is the solid that lies between the paraboloid and the sphere The graph of solid

Q: If f(x) -6₁² = 2 f'(x) =| t³ dt then

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Q: Consider moving a particle along a path given by r(t) = (e³¹, e¹, e³¹) with 0 ≤ t ≤ 1 subject to a…

A: Given that a particle moving along a path  with  subjected to force

Q: A company estimates that the revenue (in dollars) from the sale of x doghouses is given by the…

A: The objective of this question is to find the approximate change in revenue when the sales of…

Q: In 1619, the German astronomer Johannes Kepler showed that the square of the period of a planet (how…

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum 125 b)…

A: The given series

Q: Suppose the height of this motorbike's jump is given by h = -16t² +32.1t+5.7 where h is the height…

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Q: Approximate the area of the region bounded by the graph of f(t)= cos (t/2-/8) and the t-axis on…

A: The width of each sub interval is ( 9π/8 - π/8 )/4 = π/4We can calculate the height of each…

Q: solution is -3/2

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Q: A solid E is bounded by the sphere z = -x² - y² on the top and the xy-plane (z = 0). The projection…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t²…

A: The velocity function (in meters per second) is given for a particle moving along a…

Q: (b) f(x) = 1 1- x' 3 a = 2

A: Given that the function

Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: Use the alternative curvature formula k = following parameterized curve. r(t) = (4 + 2t²,2t,0) K=…

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Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

A: We have given a function that models the height in feet above the surface of the water, h(t)=-16…

Q: Suzanne must choose between two job offers. The first job offers $56,000 for the first year. Each…

A: Given that Suzanne must choose between two job offers. The first job offers $56,000 for the first…

Q: Question Given h(x) = tan(-x² + x), find h'(x). Sorry, that's incorrect. Try again? h'(x) = (2x -…

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Q: To find an antiderivative of f(x) = arctan(3x) you used integration by parts, and obtained…

A: The integration by part formula is:                             ..(1)

Q: What is the average rate of change of the function f(x) = et over the interval [-2, t]? t one -0.0…

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