Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval and find all values of c in that interval that satisfies the conclusion of the theorem. f(x) = -x² - 2 on [0,2]

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Q: Find f'(5), if f(z) = (4z² + 5x) (2x² - 8)

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Q: (Click on the graph for a larger version.) A. f3 f(x) dx = B. If the vertical red shaded area in the…

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Q: 6.6 The rational number x=p/q, where p,q are integers, satisfies the following conditions        a)…

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Q: A company determines that its woekly online sales, S(t), in dollars, t weeks after online sales…

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Q: If xy = 3 - 2x then find d'y dx² at the point (-1,5) in simplest form.

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Given function represents the position function of the projectile.

Q: The parametric equations represents a line. Without eliminating the parameter, find the slope of the…

A: given parametric equation of line is  x = 9 t -7     and   y = -5t -1 then we have to find slope of…

Q: 20. Find the foci of the ellipse whose equation is given below. (x+1)² (y+3)² 36 16 -1

A: As we know the standard equation of the ellipse is: x-h2a2+y-k2b2=1 Where the center is at h,k. And…

Q: to go to obtain an increase of Problem 2. Consider the function f(x,y) = y ¹ | ²₁ (a) What is its…

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Q: Expand the expression using the binomial theorem (2+4)*

A: As we know from the binomial theorem: x+yn=C0nxn+C1nxn-1y+C2nxn-2y2+....+Cn-1nxyn-1+Cnnyn   To…

Q: [Gradients and Directional Derivatives][S] Let h(w, f) = √(1 + wf) be a function for the height (in…

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Q: Consider the following. f(x) = In(x-3) — 1 (a) What is the domain of f? (Enter your answer using…

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Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: d the area under the given curve over the indicated interval. y=ex: [0, 4] ne area is Round to three…

A: Given query is to find the area under the curves.

Q: Answer the following and show the step-by-step solution of each: rẻ -5x+2 4x²+3 a.] limx→ 1x→+00…

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Q: A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin…

A: volume of storagr bin is volume of cylindwe +volume of cone volume of cylindwe =πr2hvolume of cone…

Q: Evaluate the function y = 2x2+2 / sqrt(x) between x=3 and x=5 using the fundamental theorem of…

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Q: 10).  Compute the Taylor series of the function around x = 1. f(x) =  x 4x − 2x2 − 1 f(x) =  ∞…

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Q: +∞ c. [to pote C. 88 e (2²+y²) dady

A: Let's solve given double integral.

Q: 2). Find the Taylor polynomial of degree two approximating the given function centered at the given…

A: According to question,Given Function,fx = cos2x

Q: Evaluate. 2 0 √2x dx

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Q: Suppose f is continuous on [5,18] and '14 3) [1²₁ /14 (a) 5 (b) 1) fort f(t) dt = 18 (c) √ ¹8: (d)…

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Q: -1 Ⓡ 6 6

A: To graph the inverse function

Q: Calculate ff f(x, y, z) dS For x² + y² =9, 0≤ z≤ 6; ffs f(x, y, z) ds = 97(e-6-1) f(x, y, z) = ez

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Q: Show if the following limits produce an indeterminate form. Then, evaluate the following limits. x 2…

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Q: 60. a. Find the linear approximating polynomial for the following function centered at a. b. Find…

A: Given that , fx=16x32 and a=9

Q: 15. Find the magnitude and direction angle for the resultant vector, u + v, given u = and v=

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Q: 1. Evaluate the following definite integrals: 1 1.- J (20-1 0 1 [ (1³ / 2. 3. (2t - 1)'dt (t³ + t²)…

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Q: Evaluate lim x-4 3 cos(x) 2x 1. limit 2. limit 4. limit = 318 3. limit doesn't exist 3 cos(4) 16 6.…

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Q: Find an antiderivative of 7 z4–9 z6 27 Antiderivative = in the variable where x > 0. Remember to…

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Q: The marginal cost function associated with producing x widgets is given by C'(x) = -0.6x + 100 where…

A: Given query is to find the cost of producing first 100 unit.

Q: 15. Determine lim x→4 1 x2-2 3 x2-8

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Q: a) 5+3+1+(-1) ++ (-33)

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Q: 13. Determine lim (6x-x²). X→-5

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Q: Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point.…

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Q: Calculate the indicated Riemann sum S3 for the function f(x)=x²-8x-33. Partition [0,6] into three…

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Q: a B What is the value of tan(a)? с b Description of image (in case it has trouble loading): A right…

A: Given that  a right angle triangle with side length. And a= 2 ; b= 3 and c= √13. And we find the…

Q: 0 1 Find an orthogonal basis for the space spanned by 0 X 2 0 2 0 , and -4 2 -6 -4

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Q: 4. When the infinite series converges, what does it seem to converge to?

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Q: (a) Solve for v(t) if the raindrop falls from rest. (2) v(t) = (b) This model assumes that the rate…

A: Basic information:  ddxaxn=anxn-1∫axndx=axn+1n+1 + Cρ is a density of the rain drop.…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: [x(t): 2+² ly(t) =…

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Q: Calculate the flux v out of the ball x² + y² + z² = 1 given that v(x, y, z) = 3zi+2yj+2 zk. a) 28T…

A: Please see the below picture for detailed solution.

Q: Find a formula for the inverse of the function. y = 6 In(x-4) y =

A: The given function y=6 lnx-4. We have to find the inverse of the function.

Q: Speedometer readings for a vehicle (in motion) at 14-second intervals are given in the table. t…

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Q: 53 6.5³ € f(x) dx = 16, then compute the value of the following definite integral. /39 If I F f(7x +…

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Q: Use Newton's method to estimate the solutions of the equation 8x²+x-1=0. Start with x = -1 for the…

A: Given Equation- 8x2+x-1=0

Q: he tangent line to s(t) a(t) at the point

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Q: Find f'(x) if f(x) = sin x+2 sec x tan x 8 cos x 2 tan² x-3 8 sin x cos x+2 sec x 8 sin x sin x sec…

A: To find the derivative of given function

Q: K Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 10.

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