K Find the average rate of change for the function over the given interval. y=ex between x= -1 and x=2 The average rate of change of y between x= -1 and x = 2 is (Round to four decimal places as needed.)

Q: Find the area of the region bounded by the graphs of the function.f(x) = . Round your answer to…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find T, N, and K for the plane curve r(t)=(8cost+8t sin t)i + (8sin t-8t cos t)j, t> 0.

A: You have asked multiple question, we will solve the first question for you. The rest can be asked as…

Q: Find the center and radius of the sphere. 2x² + 2y² +2₂² +x+y+z=25 Center = (1.1.1), radius= (Type…

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Q: Suppose the demand function for a product is given by the function: D(q) = -0.016q+ 40 Find the…

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Q: Find an equation for the tangent line to the graph of the given function at (-3,4). 2 f(x)=x²-5 Find…

A: Given query is to fins the equation of the tangent.

Q: In Exercises 1 and 2, compute u + v and u-2v. -[2][3] v= 1. u = narly enou ngga 100 sanil bas…

A: (1)   u=-12,  v=-3-1u+v=-12+-3-1=-1-32-1u-2v=-12-2-3-1=-1622    Ans

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Q: Estimate f(g(2)): First graph y=f(x) Second graph y=g(x)

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Q: An arc of length 19 meters subtends a central angle of 288° in a circle. a) Find the circumference…

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Q: 3. Evaluate the limit limx→ - sin x x² 01 0-1 00 O-∞ The limit does not exist

A: Given limit limx→0-sinxx2 = ?

Q: Graph the feasible region for the following system of inequalities. Tell whether the region is…

A: red one represents x+4y ≤12   whereas violet one represents 4x+5y≥20   region is UNBOUNDED

Q: Find the points wher the graph of the function has horizontal tangents. f(x)=4x2+4x-4

A: The point at which the first derivative of the function is equal to 0 is the point where the graph…

Q: A private school has a cost function given by C(x) = 90 + 80√x dollars, where x is the number of…

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Q: Find the cross product a x b. a = t, 8, 1 t b = (t², t², 1) Verify that it is orthogonal to both a…

A: Given: a=t, 8, 1t, b=t2, t2, 1

Q: Solve for y: O y = Oy = x = 4ln(y - 8). 1 4 ln(x - 8) x+8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy =…

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Q: Find the cross product a × b. a = (t₁3, 1), b = (12², 1², 1) 8, Verify that it is orthogonal to both…

A: Given  data :  a=t, 8, 1t, b=t2, t2, 1.

Q: Let f(x) X→ 1- = (a) Find the following limits. (If an answer does not exist, enter DNE.) lim f(x) =…

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Q: Given lim f(x) = -2 and lim g(x) = 4, evaluate: x-1 x-1 lim (-3f(x) +5g(x)) = x-1 lim (-3+5f(x)) =…

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Q: (a) In order to express the function y=(2t^4−8)^5 as a composition of two functions the outer of…

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Q: Let f(x)=5x+4 Let g(x)=ln(x)+3 Find the following: (a) g(f(x))= (b) f(g(x))= (c)…

A: f(x)=5x+4g(x)=lnx+3(a)for g(f(x)), put x=5x+4 in g(x)

Q: use the complex zeros to factor f(x)=x4+122x2+121

A: f(x)=x4+122x2+121we know -1=i

Q: J = (x)\, mil 6. Find an equation of the tangent line to the curve y = √ at the point (4,2).

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Q: Video Example Show that Solution 9x² - 4y² lim (x, y) (0, 0) x² + y² Let f(x, y) = (9x² - 4y²) (x² +…

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Q: Given lim f(x) = 5 and lim g(x) = -1, evaluate: x-7 x-7 lim (g(x) In (4f(x) — 4)) = x-7 lim…

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Q: Consider the curve y = x² + 3x + 4. (a) Find the slope of the secant line to the curve through the…

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Q: Integrate/Evaluate the following: S dx (a) (b) 25-x2 X x³ dx 3 (x²-1)2

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Q: Consider the following graph. y 10 5 JA -5 5 -5 -10 -10 10 X ℗ Use the given graph of the function…

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Q: The top and bottom ends of a windshield wiper blade are 31 inches and 13 inches, respectively, from…

A: Given: The top and bottom ends of a windshield wiper blade are 31 inches and 13 inches,respectively,…

Q: Find the first partial derivatives of the function. f(x, y) = x6 + 3xy⁹ fx(x, y) fy(x, y) - "

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Q: Q1: Gasoline sold for RMB 8.72 per litre in Beijing and US$ 5.49 per gallon in Seattle. Find the…

A: Using converter price and quantity

Q: Determine the average rate of change of the following function between the given values of the…

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Q: Use the chain rule to find dz dt = Z = х- у x + 6y dz dt x = ent y = ent

A: Given z = x - yx + 6y x = eπty = e-πt

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose that M is the function that computes how many miles are in î feet. Find the algebraic rule…

A: Given query is to find the formula for mile in terms of feet.

Q: ind an equation of the plane. The plane that passes through the line of intersection of the planes x…

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Q: Can someone please help me

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Q: Find the cosine of the angle between the normal vectors to the planes x+y+ 2z = 3 and 2x -y + 2z = 5

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Q: Use the graph below to fill in the missing values. -1 5 3 7 f(0) = f(x) f-¹(0) = 1 2 3 f(x)=0, x=…

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Q: ector equation for this line is r(t) = (5, -4, 3) + t1, 4, - ½)

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Q: Solve the following system with inverse matrices. Show the algebraic set-up of your system, find and…

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Q: Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1…

A: The height of the rock is given as: ht=-5t2+20t+25 The instantaneous velocity of the rock at time…

Q: 2. g(x) = x³ +5x²

A: g(x)=x3+5x2formuls for difference quotient=g(x+h)-g(x)h

Q: A graphing calculator is recommended. If a rock is thrown upward on the planet Mars with a velocity…

A: As given height of the particle is y=14t-1.86t2 after time t of throwing.

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Find the range of f(x) = 23 e*+3

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Q: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f…

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Q: the time required for an investment of 3,000 dollars to grow to 12,000 dollars at an interest rate…

A: Given query is to find the time required to reach the investment to 12000.

Q: State the derivative. Do not simplify. f(x) = - x² +3 X

A: INTRODUCTION A derivative of a function is a measure of the rate of change of the function with…