Find an antiderivative F(x) with F'(x) = f(x) = 5e" and F(0) = 0.

Q: Find the volume of the solid obtained by rotating the region = bounded by the x-axis, the y-axis,…

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Q: Find the limit of f(x) = lim f(x) = -5 9√x+x 3x-9 X→∞ (Simplify your answer.) as x approaches co.

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Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

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Q: Find the centre of mass of the region between y = x x² and y = x³ from x = 0 to X = 1.

A: The objective of this question is to find the centre of mass of the region between the curves y =…

Q: Find the center, foci, and vertices of the ellipse. Graph the equation. 4(x+4)² +8(y - 3)² = 32 Find…

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Q: Find all exact solutions on the interval 0 < 0 < 360°. If there is more than one answer, enter them…

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Q: 8. p-series below: (a) n=1 Use this fact to find the sum of each series below. (You may express your…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

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Q: Find the second derivative of the following functions: a. f(x) = x5 + sin x b. f(x) = x² + == x c.…

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Q: Find the absolute max. and min. of each function y=√4−x^2, (−2,1)

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

Q: is it 3and -2 for A?

A: A critical point of a function f(x) is a coordinate where the derivative f'(x) =0 for the x…

Q: d. y = 2x+1 x²-4 5x+1 e. y = 2√x-1 f. y = sin x ln x-1 x²+1/

A: To find the derivative of the following functions.

Q: A 100 m long rope hangs from the top of a mine shaft, and is attached to a crate full of coal. The…

A: The objective of this question is to calculate the total amount of work done to lift the rope and…

Q: Solve the rational inequality x²-9 x² - 49 -≤0.

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Q: Two cylinders are given. The larger cylinder is a dilation of the smaller cylinder. Part A:…

A: Smaller length = 2mLarger length = 9mVolume of the smaller cylinder = 24 pi m3

Q: Question 1 If you know that Q(x) is a quadratic function and that Q(8) = 7, Q(7) = 2 and Q(1) = 6…

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Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

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Q: The system of differential equations : has the solution Y = C₁ et V₁ + C₂ ezt V₂ + C3 e¹³ V3 where…

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Q: Consider the parametric curve: x Y 4 +² +³4t At which t value(s) is the tangent to this curve…

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Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find parametric equations for the following curve. Include an interval for the parameter. The left…

A: We have to use the concept of parametric equation

Q: Find the radius R of convergence for the series R = n=1 2x+1 87+1 n8

A: The given power series .The aim is to find the radius of convergence of the power series.

Q: 8. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval [0, π/2], are…

A: The given functions are the inner product of two functions f and g on the interval [a, b] is the…

Q: lim n→∞ (1 + 1/2 ) ² = 2n

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Q: 1. The general solution of the system [x' = y, y' is given by x(t) = C₁ cost + C₂ sint, y(t) = C₁…

A: x'= y..........(1)y'= -x.........(2)

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: y = xe-x , 1 ≤ x ≤ 7

Q: 9. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval 0, π], are…

A: Given that the function are

Q: Find all exact solutions on the interval [0, 27). If there is more than one answer, enter them as a…

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Q: Given f(x) = -√√/16 - x is concave up on its domain, what is an estimate for f (4.9) using the local…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,

Q: Find the interval I and radius of convergence R for the given power series. (Enter your answer for…

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Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

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Q: Find all solutions exactly on the interval [0, 27). If there is more than one answer, enter them as…

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Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

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Q: 1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke…

A: Here given a different sentences.The objective is to check that the given sentences are valid,…

Q: Find the domain of f(x). f(x) = Interval 3x - 5 x² + 2x - 35 Answer Attempt 1 out of 2 2 Answer…

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Q: When solving the auxiliary equation associated with the differential equation 3y"+2y"=0 it is…

A: .

Q: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

A: Given,

Q: Find the area under the given parametric curve over the given interval. x = 4t³ - t²; y = t4 + 2t²;…

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Q: k. y = ln x 1. m. y = y = 5 cos x + 8 lnx + 3x³ 3x¹+3x²+1 x

A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

Q: Evaluate the following limits algebraically. 2. lim x---> 2^-      (x+4) / (x^2 + 2x - 8) 4. lim…

A: To evaluate the following limits.

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

A: Given,a(t)=t+4v(0)= 70=&lt;t=&lt;10

Q: Evaluate the limit, use L'Hospital's Rule when possible. limx→0 5x In(x+2) O-5 01/2 0 5 Not Possible

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. an = tan -1…

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Q: The function y(x) saifies the following equation: Find an expression for dy dx 5 x² − 2xy+3y² − 3 x…

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Q: Find an antiderivative of the function h(y) = 3y² — y6. An antiderivative is

A: .

Q: Evaluate the iterated integral. LT (3) (3x - 2y) dy dx

A: we need to evaluate the given double integration.

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: The objective of this question is to find the critical numbers of the given function f(x) = 12x -…

Q: Find the area A of the region that is bounded between the curve f(x) = −2 sin (2) over the interval…

A: Given that the region bounded by the functions  and  over the interval