Find the volume generated by revolving the area bounded by parabolas y? = x and y = x² about x = -1. Use ring method.

Q: Evaluate 2x(x2 + 2)*dx

A: First I have used  a substitution and made integral easy and then solved it.This is the process.

Q: 2. Solve x? – 6ax+ 2 = 0, where a>1 is a constant. -

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Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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

A: We need to give constraint equation.

Q: A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming…

A: Let's find.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given :r(t)=cos(πt)i-ln(t)j+t-14k ; t0=15To find : The domain of r(t) and the value of r(t0)

Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). 13 r(t) = t°i+ t°j K(t) =

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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: 9x² = 164 -8y² + 36x + 64y

A: The given equation is: 9x2-8y2+36x+64y=164...(1)

Q: Find the profit function for the given marginal profit and initial condition. Marginal Profit…

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Q: dx メ-1

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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: Q2) Convert the polar function r tan20 to cartesian. %3D

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

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Q: 2x + 6 Consider the function f(x) = . For this function there are two important intervals: (– ∞, A)…

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Q: - Determine whether L'Hospital's Rule applies to the limit below, then evaluate the limit 3r3 – 2x…

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Q: Starting at age35 ​, you deposit​ $2000 a year into an IRA account for retirement.  Treat the yearly…

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Q: Q11. Suppose z = f(x, y), x = g(t), and y = h(t) satisfy: h(7) = -2 h'(7) = 1 f-(2, –2) = 2 fy(2,…

A: Suppose z=fx, y, x=gt, and y=ht satisfy: g7=2, h7=-2, fx2, -2=2g'7=-3, h'7=1, fy2, -2=0By using the…

Q: 9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2, 1).…

A: We have to find the equation of the tangent.

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: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

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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Q: 1. メーメー2 xペー5x+6

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given that the population of mosquitoes in a certain increases at a rate proportional to the current…

Q: Evaluate the definite integral. e14t i + e¬1j +t k )dt O el4 (e-- – 1) j + k i+ 14 (el4 – 1) i- (e -…

A: Evaluate the definite integral

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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Q: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

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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: The function f(x) = – 4x* + 6.24x² + 53.784x + 1.62 is increasing on the open interval ( It is…

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Q: 3. Consider the graph of y = ln (x) + 1. Calculate the area enclosed by the curve y= ln (x) +1 and…

A: The region is bounded by y=ln(x)+1 and the y-axis between the lines y=1 and y=2

Q: A Hippogriff is a magical beast that had the front legs, wings, and head of a giant eagle and the…

A: Required formula:  Logistic growth model: Nt=K1+K-N0N0e-rt Where,  r = Exponential growth rate…

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 140 when p = $5…

A: Here, dxdp=10p-5⇒dx=10p-5dp⇒∫dx=10∫1p-5dp+C...(1)

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. + dy

A: Line integral

Q: Consider the angle shown below that has a radian measure of 0. A circle with a radius of 2.7 cm is…

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Q: 14. E sin x dx cb

A: According to the guidelines, I am answering first question. Please repost the remaining. Explanation…

Q: Problem: At time t = 0 there are 10 person in a community of 1,000 people who has the flu.…

A: Required formula:  Logistic growth model: Nt=K1+K-N0N0e-rt Where,  r = Exponential growth rate…

Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

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Q: 36 – x2 – y? and S2 be t Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the…

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Q: velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2 - 2t…

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Q: Find the arc length L of the graph of r(t). r(t) = 4 cos(t)i + 4 sin(t)j+ tk, 0<t< 2m L

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). r(t) = e*i+etj K(t) =

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Q: 12. L(s? – 1) sds 13. (1² – #) dt

A: ∫xndx=xn+1n+1+C , C is a constant for any real number n.

Q: 1. a) Find the linear approximation of f(x) = Vx at x= 27 %3D b) Use it to approximate V26.9

A: To find linear approximation of given function

Q: 12 12 f(x) dx = 16 and 9. If f(x) dx = 5, find the following. %3D f(x) dx

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Q: Since f'(x) is a function, f'(x) has its own graph, one that is based on the behavior of f(x). True…

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Q: 3 2. (8x2 – 3x) (12x2 – 3) dx

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Q: Find the particular solution of the following ODE given that y(0)=0 and y '(0)=0: d'y +y=e* dx

A: A Particular solution of the differential equation is a solution of the form y= f(x) , which don't…

Q: Find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal Cost…

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Q: 6n Q4. Determine whether the infinite sequence converges or diverges. /Зп? + 7 n=1 If it converges,…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: Find Maclaurin series.