For the following exercises, the vectors u and v are given. a. Find the vector projection w= proju v of vector v onto vector u. Express your answer in component form. b. Find the scalar projection compu v of vector v onto vector u.

Q: True or False? The function f(x)=√4-x2 is guaranteed to have an absolute maximum and minimum on the…

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Q: A car travels down a straight road. Let s(t) be the position (in meters) of the car at time t…

A: Here given thats(t) =position of the car at time tgiven initial position s(0) = 4minitial velocity…

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: The given integral ∫cos x7sin2x+8sin xdx. We have to find the solution to the integral. Formulas…

Q: What is the volume of the solid generated when the region bounded by the graph of y = 4x, the…

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Q: Find the volume of the solid enclosed by z = 6, y = 0, y = 16-r², and z + y = 22

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Q: Find the point(s) of intersection 2x + 7y = 10, x-1 7 (x, y, z) = (if any) of the plane and the…

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Q: Evaluate the Limits: a) limt->-1(t2+3t+2)/(t2-t-2) b) limx->9 (9x-x2)/(3-x1/2) c) limx->-inf…

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Q: Find all critical points of g(t) t = t = = This critical point is ---Select--- (smaller value)…

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Q: Consider the following series. Answer the following questions. Σ (x + 7) n 2n n=0 1. Find the values…

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Q: Find an equation of the tangent line to the curve at the given point. f(x) = 4x²-x³, (1, 3) y =…

A: Solution: f(x)=4x2-x3, (1,3)

Q: Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the…

A: The given demand function is: g=408-0.3p

Q: Find the derivate of this function]: 2 a) f(x) = 4x² + x + 9 at -5 f(-5) = b) f(x) = √√√x at 16 F'…

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Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g'…

A: Derivative

Q: Find the following limit. lim V

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Q: Please answer both. #1-The length of a rectangle is increasing at a rate of 6 cm/s and its width is…

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Q: Evaluate the double integral over the given region R R (18y²-14x) DA R: 0≤x≤4, 0≤y≤2

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Q: that the cords have been disconnected from the device. "Computer, how do I plug in these cables",…

A: f(x)=ln(3x) f'(x)=313x = 1x f'(c)=1c   it is required Red cord.

Q: Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the…

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Q: 1 Find the area of the surface generated by revolving the curve x = 3 cos (3t), y = 2 + 1 sin (3t)…

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Q: Replace the Cartesian equation x = y with an equivalent polar equation.

A: given x=y

Q: The daily cost C (in dollars) for a manufacturer to produce a electronic video components is given…

A: Solution: Given:C(x)=2000ln3x2-5003

Q: A meadow has the shape shown, where the measurements shown were taken at 30-foot intervals. Use…

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Q: Find the volume of the region bounded above by the surface z = 2 cos x cos y and below by the…

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Q: Find a function of the form y= A sin(kx) + C or y= A cos(kx) + C whose graph matches this or -6 5₁…

A: We are asked to find the equation of the graph

Q: Find the critical points in the domain of the function f(x) = 8x³ - 7x.

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Q: 4. Differentiate = ex) in (ex + xe (b) find dy by implicit differentiation 2 ху √x² + y²

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Q: Use logarithmic differentiation to find the derivative of the function. y = (tan(x)) 5/x y' =

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Q: Consider the function f(0) = 4cos2²0 + 4sine. (a) Find f'(0) = (b) Determine the critical points of…

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Q: Find the local maxima, local minima, and saddle points, if any, for the function z = 5x³ - 30xy -…

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Q: Find the derivate of this function]: a) f(x)= = e* b) f(x) = 6x²2x₁ F'(x) = c) f(x) = (6x - 5)(2x…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

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Q: Find the length of the vector. v = (4, 0, -2,-5) ||v|| =

A: v=(4,0,-2,-5)

Q: The form of the partial fraction decomposition of a rational function is given below. A = B = C =…

A: Given : A = 4  B = -3 C = 0

Q: 2r cos 0 Replace the polar equation r= (csc 0)3e2rc with an equivalent Cartesian equation. T

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Q: The position function of a particle is given below. s(t) = t³ + 6t² − 33t, t ≥ - 0 When does the…

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Q: b) y = 8 + 1 4x² on [1,2]

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Q: Find the derivative

A: Given: h(x)=(x-3)e5x-7x4

Q: -9 dx (3x + 1)² 1

A: Solution: ∫1∞-9(3x+1)2dxTake the constant out=-9×∫1∞1(3x+1)2dx

Q: Find the surface area for the portion of the surface z − 2x + y2 = 21 that lies above the triangle…

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Q: (d) B dy dx 1- x - y x + y

A: ode

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

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Q: Differentiate the function. f'(x) = f(x) = e5

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Q: I. INTEGRATING FACTORS BY FORMULA 2 1/2 x 2x/x-2

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Q: Match each of the following conditions with an equation. f(x) = 24x - 4 fil(0) f(0) = f(0) = 0 = y =…

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Q: Evaluate the integral Answer: z³ +66 x² + 6x + 8 S dx.

A: To evaluate the integral

Q: A metal cube dissolves in acid such that an edge of the cube decreases by 0.70 mm/min. How fast is…

A: We have to find the rate of change of volume.

Q: A function f is given, and the indicated transformations are applied to its graph (in the given…

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Q: Solve the following initial value problem using Laplace transform method: y"+3y'+2y=cos 2t y(0)=-1…

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Q: The graph of f(x) is given on the grid. Graph ƒ'(x), its derivative. 5- -5 -4 -3 -2 -1 3 2 1 -1 -2…

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Q: As you move through the first gate, you can see another gate not far in front of you. You approach…

A: Given: g(x) = x+3x2-9 The function does not exist when their denominator is zero. That is,…