Use the Chain Rule to find dz/dt. z = xy9 − x2y,    x = t2 + 1,    y = t2 − 1

Q: Question 15 of 16, Step 1 of 1 18/29 Correct Among all rectangles that have a perimeter of 84, find…

A: Topic- Application of derivatives Let L=Length of rectangle W=width of rectangle Perimeter of…

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Q: 5. Find all constants a, b that make f continuous everywhere. (Use limits and definition of…

A: With the help of limiting criteria we have to find the values of a and b.

Q: y = √x y = x² 1. 0.8 0.6 0.4 0.2 0.2 y= √x 0.4 y=x² 0.6 0.8 1. 1.2 x

A: The equation of the curves are: C1: y = xC2:y = x2 Axis of Rotation: y-axis Formula Used: Washer…

Q: f(x) = √8x-6, g(x) = x² - 16, (f + g)(x)

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Q: In each of Problems 1 through 8: Ga. Draw a direction field for the given differential equation. b.…

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Q: A cell phone plan has a basic charge of $30 a month. The plan includes 400 free minutes and charges…

A: Given problem:- A cell phone plan has a basic charge of $30 a month. The plan includes 400 free…

Q: Determine the point(s) at which the given function f(x) is continuous. f(x) = 15x - 21+5 sin (2x)…

A: GIven function:- fx=5x-2+5sin2x

Q: Find the projection uy = (x, y) of u = (6, -7) along v = (1,2). (Use symbolic notation and fractions…

A: Topic - Projection of vector Projection of vector u along v=u.vv2v

Q: 3) Determine the speed of change of volume of a rectangular parallelepiped, knowing that the edges…

A: Let the length of base edges and vertical edge are x, y and z respectively such that dxdt = +2…

Q: #4 The function E (t) = 4.66459 t4.4054 describes the available capacity (in kilowatt hours = kWh)…

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Q: 2) Suppose that a fashion company determines that the cost, in dollars, of producing x cellphone…

A: NOTE: Refresh your page if you can't see any equations. . take x=400

Q: mation 9. y'-y = 2te²¹, y(0) = 1 2

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Q: III. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e* + c)

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Q: Use the final value theorem, the final value of f(t)=6. (et +2) - 10 is.....

A: Final Value Theorem:- For a function or system  f(t) is given by f(∞)=lims→0sF(s), where F(s) is the…

Q: 1. f(x) = (x+4)² 2. f(x)=√x +3 +40 CHI

A: 1. Parent fuction will bef(x) =xto understand better I have drawn the graph using online tool (will…

Q: Find a parameterization for the curve shown in the figure below. r(t) = where = -1 1,0 -1 <t<

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Q: Find the unit normal vector for the vector-valued function r(t)=(t^2-3t)i + (4t+1)j and evaluate it…

A: Given data:- Vector-valued function, rt=t2-3ti + 4t+1j Evaluate at t=2

Q: 1) f(x) = *-1 x+2 Find a) f(1) b) f(a + 1)

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

A: To find the difference quotient of the given function.

Q: Set up an integral representing the area A of the region enclosed by the given curves. y = 5x,   y =…

A: Given :

Q: Find the volume of the solid that results when the area of the region enclosed by y=√√sin x and the…

A: Concept: Volume by integration: The volume of the solid produced by the region under f(x) centered…

Q: x-2 x-2x²+x-6 5. Evaluate: lim

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Q: a) Complete the table below given f(x)=sin(3x)/x Round your answers to six decimal…

A: Compute the table for f(x)=sin(3x)x

Q: A wheel of radius 14 inches is rotating 12°/sec. What is the linear speed in in/sec and the angular…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x and y = √x about the…

A: Given problem:-- Find the volume of the solid obtained by rotating the region bounded by y = x and…

Q: A) 2xe-x(x + 2) 30) u(1) = 2, u '(1) = -7, v(1) = 7, v '(1) = -3. d at x = 1 dx u B) 2xe-X(2-x)…

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Q: Solve the inequality involving absolute value. Enter the exact answer in interval notation. To enter…

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Q: A sports franchise revenue can be modeled by the function R(t) = 337 + 8t. Their operating costs are…

A: Given data:- Revenue function R(t) = 337+8t Cost function C(t) = 245+20t

Q: Find the distance of the point (4, 2, −4) from the line r(t) = (−1+ 2t, 1+ 2t, 7 – 3t). Answer:

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Q: Find the shortest distance between the (entire) line L1 passing through the points A(1, 1, 2) and…

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Q: Use function composition to determine if f (x) ar (a) Yes, they are inverse functions. (b) No, they…

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Q: Let f and g be functions defined as f(x)=x²- 2x + 4 and 25 4 DNE 1 g(x) = 3x² + ²3. If h(x) ≥ g(x)…

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Q: observing the outside temperature rise. What is the relevant independent variable here? The…

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Q: 5. Find and sketch the domains of the functions of two variables below. Sketch the boundary with a…

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Q: 5000 liters of the toxic substance Trioxin was dumped into the local swamp at the beginning of the…

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Q: The graph below is the function f(x) -5 -4 -3 -2 -1 Find lim H-2 5 4 Find f(2) 3 2 1 -1 -2 -3 S 1 2…

A: Solution:

Q: Which of the following is/are signified by lim f(x) = ∞00? I a As a approaches a, the value of f(x)…

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Q: Find the Average Rate of Change of the following function (That is, from t = 2 to t = 5.) over the…

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Q: Find the set of all solutions of each of the following differential equations.  y" =32.

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Q: Write a function of the form f(x) = csc (Bx-C) for the given graph. 3 2 1 0 -1 -2 -3 F 12 5п 12 3πI…

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Q: In Problems 1-6, identify the equation as separable, linear, exact, or having an integrating factor…

A: Dear Learner,We expert are following bartleby expert guidline so we can answer only one question.…

Q: For what values of a and b is the following function continuous at every x? - 10 f(x) = axb 4 x≤ -3…

A: Function to be continuous at point x = a, it must be defined at that point.

Q: 1. Find the derivatives of the following function (a) y=4²+2

A: Given Equation: y=4x2x-3xx+2xx          .....................(1)y=2x+3x2+x+1…

Q: Given x and f(x), fill out the rest of the table. X -2 -1 f(x) f(x) - 1-6 f(x - 1)-7 -f(x) 5 f(-x)…

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Q: Find a formula for the described function. A rectangle has area 16 m². Express the perimeter of the…

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Q: Express 0.96 in the a/b where a and b are integers such that b=0

A: Given data:- The given equation is 0.96,

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: E] Find the zeros of the function f(x) = 3x² - 6x + 2 F] Find the points of intersection of y = x² -…

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