APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write your answers on a separate sheet of paper. a. S(5x + 4)*dx c. S sin"(x) cos(x) dx d. (-de

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Given that     D(x) = -3x/10 + 8     S(x) = x/5 + 3

Q: 7 5 5. sec '(In t) tan° (In t) dt t

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Q: Find the particular solution of the following ODE given that y(0)=0 and y'(0)=3: d'y dy +10 +25y = 0…

A: Explanation of the answer is as follows

Q: 1. Find the absolute maximum value of the function f(x)=x³ – x² – - x on the interval -1<x<10.

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Q: B. Solve the following problems using differentials and linear approximations. Show complete…

A: (a) The given function is: f(x)=x3 The formula for the linear approximation at x=27 is given by:…

Q: The demand curve for a certain product is given by p(q) = 517- q. The supply curve is given by p(q)…

A: We have to find the consumer surpless.

Q: d d Calculate ri(t) · r2(t)] and r(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Let C1 be the curve with parametric equations x = cost, y = sint – t, where t e [0, 5]. (a) Find the…

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Q: Formulate a linear programming problem that can be used to solve the following question. A dealer…

A: topic - linear programming

Q: he acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

A: Given query is to find the velocity function and the distance traveled.

Q: 4. sec 4x tan 4x dx

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Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: For what values of the constant k does the Second Derivative Test guarantee that f(x.y)=x+kxy+y will…

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Q: Obtain the value of P3 (x) using Rodrigues' formula d" P,(x) = (x² – 1)" (2")n! dx"

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Q: e Newton's method to approximate a root of the equation 5x+ 7x +3 = 0 as follo 1 = -1 be the initial…

A: answer is in next step

Q: 6 sin z Let f(r) = 6 sin z + 2 coS T Then f'(x) = The equation of the tangent line to y = f(z) at a…

A: Given query is to find the derivative of the function.

Q: Find the curvature of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the point t %3D Give your…

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Q: 2. Sin 2x dp X UIS 6.

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Q: Problem 4. Which gives the inverse transforms of the given s-domain function 1.88sin 2.67t -…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk K(t)…

A: By using the formula kt=r't×r''tr't3 to find kt.rt=4 cos7t i+4 sin7t j+3t k

Q: The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

A: Given: The radius of a sphere is increased from 20cm to 20.2cm. To find: Estimate the change in…

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

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Q: Solve the Laplace Transform of the given function 6e5t cos(2t) – e7t

A: Solved below

Q: S csc2xdx cosx O sinx+C O -cotx+C O -cotx

A: By using standard formula.

Q: 1. Consider the curve defined by 9x2 – 16 y² + 36x + 96 y– 252 = 0. a) Write the equation of the…

A: To solve the following problem

Q: Given the e dz nd y, find ar

A: Given: xlny=zArctan3zy

Q: Given that u= and v= and that u.v= 199 determine the value of the constant A. Answer:

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Q: cos e d0 Jo 1+sin? A 2

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Q: 2 Find the general antiderivative of f(x) = 5x* + 4 + C

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Q: 13. Explain in your own words what a limit is. Use several diagrams and be sure to consider lim…

A: This is a problem of limit. Based on the general formula we will answer the question.

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Q: A bacteria culture is growing at a rate of r(t) = 8e0.6t thousand bacteria per hour after t hours.…

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Q: 2t2 + 3, y = 6t – 1 at the point whose 3. Find the equation of the normal to the curve defined by x…

A: Explanation of the answer is as follows

Q: 1+x+y dzdyax Jc JO Jo

A: To evaluate the given iterated integral.

Q: Find for the Implicit function: dx x2 – sin(xy) + y? = 5xy

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 3 r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: . Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

A: (a)x=7sint , y=t2+1 at (0,3)sint=x7 t=sin-1x7 now, y=t2+1substitute t=sin-1x7  in  y=t2+1y=sin-1x7…

Q: 2n n E(-1)"; n! n=1

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Q: Evaluate the limit tan x lim z0 2x

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r"(t)||3 r(t) = e*i+e*j K(t)

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Q: 4. 7 [fx)dx = - 7, r(x)dx = -7, and = 7. Use these to complete parts (a) through (f). The functions…

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Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: I have appended the formula used in the solution part.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t*|dt (25;² + 1) – 1 3j2

A: The given integral,                        ∫05ti+t2jdt

Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

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Q: 4. coth(ln x)

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Q: 12. The Statue of Liberty is 150 feet tall and stands on a 150 foot pedestal. How far from the base…

A: First supposed that an angle as alpha then use trigonometric ratio  and make a relation between x…

Q: Find the volume of the solid generated by revolving the area bounded by y = x³ and x? = y3 about the…

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Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

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Q: Solve for the function that will satisfy the given Bernoulli Differential equations: dy/dx + (1/x)y…

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Q: For what values of x in [0, 2T does the graph of f(x) = x + 2 sin x have a horizontal tangent? List…

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