1. Find a particular solution to y" + 4y + 4y= 25 cos(t). Solution yp(t) =

Q: Consider the function f(x) = x² − 72x² + 5, −5 ≤ x ≤ 13. This function has an absolute minimum value…

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Q: 1. We are interested in evaluating the integral √ √9-² da. Note that this integral gives you the…

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Q: Let s(t) = 6t³ + 9t² - 216t be the equation of motion for a particle. Find a function for the…

A: Given data:- The equation of motion for a particle is, st = 6t3+9t2-216t

Q: Find the equation for a polynomial f(x) that satisfies the following: Degree 3 ■ Zero at x = 2 ■…

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Q: How long is the radius of the circle with center at (-4,5) and tangent to the y- axis?

A: Given query is to find the radius of the circle.

Q: 5. f3-* dx 6. S √ √√9-t² 7. S- 1-e²t dt dt

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Q: Find the following using the table below. x 1 f(x) 3 f'(x) 2 2 3 4 2 4 1 4 1 3 g(x) 4 3 1 2 g'(x) 2…

A: Given that hx=fx.gxh'x=f'x.gx+fx.g'xh'2=f'2.g2+f2.g'2h'2=4×3+2×3h'2=12+6h'2=18

Q: A light truck with manual transmission has a circular brake drum with a diameter of d 300…

A: Solved Below

Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation. 11- X

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Q: Consider the following figure. To -6 -5 -4 -3 -2 -1 11+ 10+ 9+ 8- 7+ 5 5+ 4- لیا 3- 2+ 1- O -1+ 2 N=…

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Q: Find the GS for y""+y"+y' + y = 1−x + e* - COS X

A: Given differential equation y'''+y''+y'+y=1-x+ex-cosx

Q: Problem 5. Consider the curves y = 4x, y = 1/x and y = 1. (a) (b) Graph all the curves to visualize…

A: Let's graph the given curves and find area of region.

Q: Evaluate the following integrals using substitution(s): Might want to use your own paper 1. S - x²…

A: According to guidelines we can solve only first question .solution:-(1)∫x31-x2 dxlet 1-x2=t,…

Q: Find and classify (as a relative maximum, etc) all critical points of j(x, y) = 2x³ + 3xy + 2y³.

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Q: Find the limit. 3 - 3 tan(x) lim x→→/4 sin(x) - cos(x)

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Q: did

A: Yes, you are right there is some mistake in part e. so, I am rectifying it in next step. Sorry for…

Q: Find the general solution to the given equation 2y" + y − 3y = 0

A: The objective of the question is evaluate the given differential equations.

Q: The cube root of 27 is 3. How much larger is the cube root of 27.5? Estimate using the Linear…

A: We need to find △f.

Q: 27-30 Compare the values of Ay and dy if x changes from 1 to 1.05. What if x changes from 1 to 1.01?…

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Q: 3. For the function f whose graph is given, state the following. Motown (b) (a) lim f(x) 818 lim…

A: We need to find out the limits from the graph.

Q: Find the linearization at x = a. f(x) = 3₁ a=5 (Express numbers in exact form. Use symbolic notation…

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Q: Find three positive numbers whose product is 117 such that the sum of their squares is as small as…

A: Let three positive numbers are x,y and z

Q: Find the interval(s) on which f(x) = |x² - 9| is differentiable. Enter your answer using interval…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Find the volume of the given solid. Diag 47 12 under the plane x - 2y + z = 5 and above the region…

A: The solid is under the plane is x - 2y + z = 5 and above the region bounded by x + y = 1 and x2 + y…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Differentiate. f(x) X x+ C X

A: Topic -Derivative of a function We are given, f(x)=xx+cxwe know thatddxuv=vu'-uv'v2    [ u and v are…

Q: Determine the equation of a plane tangent to a given surface at a point. Find the tangent plane to…

A: The given equation is  z=4ycos(2x-5y) at (5, 2, 8) Find the equation of tangent plane.

Q: Calculate the partial derivatives of a function of two variables. Given f(z, y) = 10 + 4y + 7zy,…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Estimate using the linearization L(x) of f(x) (Use decimal notation. Give your answer to five…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Solution:

Q: A constant force of 50 lb is applied at an angle of 48° to pull a handcart 41 ft across the ground.…

A: Force, F= 50 lb  Angle with base = 48°  Displacement = 41 feet

Q: Evaluate the double integral. J log (6) 4y 5x5 +1 D = {(x, y) | 0 ≤ x ≤ 1,0 ≤ y ≤ x²} dA, D=

A: NOTE: Refresh your page if you can't see any equations. . limit of x and y are

Q: Write the particular solution of the first order linear differential equatic + x)dy + (y - cosx) dx…

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Q: Find the maximum value M of f(x, y) = x³y³ for x ≥ 0, y ≥ 0 on the line x + y = 2. (Use symbolic…

A: Given that fx,y=x5y3  ,x≥0,y≥0 To find : Maximum value on the line x+y=2Solution :we know that…

Q: Find the volume V of the solid obtained by rotating the region bounded by the curves y = 6/x, x = 1,…

A: Topic = Volume

Q: b. If the surface area of the rectangular box is 24 square feet, find dy when x = dx 2 feet and y =…

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Q: 23-24 Find the local maximum and minimum values of f using both the First and Second Derivative…

A: To find the local maximum and minimum values of f by using both the First and Second Derivative…

Q: Given the demand function D(p)=√√375 - 4p, How many products will be sold if the price is $2? Find…

A: Let's find elasticity Function and elasticity at price $2.

Q: a) y = cos 2x on [0,1] b) x= on [1,10]

A: 6) a) y=cos(2x) on [0,π] the length of the curve is given by  L=∫ab(1+f'(x)2) dx here f(x)=cos(2x)…

Q: Differentiate the following. (a) y = sin(x4) (b) y = sin(x) Solution (a) If y = sin(x4), then the…

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Q: 6. A curve passes through the point (4, 2), as shown in the figure. If from any point P on the…

A: Let's find equation of curve.

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 64°C, it…

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: 37-38 Explain, in terms of linear approximations or differen- tials, why the approximation is…

A: We are required to prove that 4.02  ≈2.005 using the method of linear approximations

Q: Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to…

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Q: Find Cross Product Find the cross product u x 7 where u = 6i +8j +8k and 7 = 6i +8j +8k and 7 = (4,…

A: Topic = Vector

Q: Draw - 7T in standard position. Answer in radians, the □ is already given. 4 -5 -4 -3 -2 -1 Clear…

A: We need to plot the angle :

Q: Use the tangent plane to approximate a function of two variables at a point. Use a tangent plane at…

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Q: Perform the following operations on the vectors μ = (3,-2), 7 = (0, −5), and w = (-4,-2). ü.w=…

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Q: Find the differential of the function f(x, y) = x√y at the point (2, 7) using Az = 0.3 and Ay = 0.15…

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