Let C be the curve y = 4x³ for 0≤x≤ 1.2.

Q: Find all possible functions with the given derivative. f'(x) = x5 f(x) =

A: Given function

Q: DOES THE SERIES 8101800 n=o n√nti 2n √n+3 CONVERGE? WHY OR WHY NOT?

A: To determine whether the following series converges.

Q: Find all horizontal asymptotes of the following function. f(x) = 3(x − 1)(x + 1) 2(x - 1)

A: f(x)= 3(x-1)(x+1)/2(x-1)We have to find horizontal asymptotes

Q: Evaluate the integral using integration by parts √4x5 4x*e* dx

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Q: Find the volume of the solid bounded below by the plane z = 2 and above by the sphere…

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Q: Find the area in the third quadrant bounded by the curve y ·x³ + 5x² -x-3.

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Q: (d) k=1 5k 8k+6

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Q: Given the velocity v = ds and the initial position of a body moving along a coordinate line, find…

A: Given the velocity function    v(t) = 9.8t +4 .................(1) and     s(0) = 10

Q: I plugged it in to my assignment and for cos(a-b) it says it's a -4 and not a +4. But thank you so…

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Q: Find all y-intercepts of the following function. Express your answer as a coordinate

A: The y-intercept is the point on the graph, where the x-value is 0.

Q: Το test the series Σ for convergence, you can use √k² k=1 the P-test. (You could also use the…

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Q: Find f F · dr' for F = -2y7 – 2x 3 – 5z k if C is the helix x = cost, y = sint, z = t, for 0 ≤ t ≤…

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Q: The volume V, in liters, of air in the lungs during a three-second respiratory cycle is approximated…

A: Given: The Volume (V) of air in the lungs during a one second respiration cycle is

Q: Use the given information to determine the remaining five trigonometric values. Rationalize any…

A: Given, that is A is in quadrant 2.

Q: A company has total cost function C(x) (in dollars), where is x is the number of items. C(x) = 300+…

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Q: Use the graph of the function g shown to estimate the function value g(2.7). Find the function…

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Q: 1 = (x + ¹)² + ²2(x + 1)² (2) Calculate the arc length of y = over the interval [1, 4].

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Q: Evaluate the integral by reversing the order of integration. y cos(x²) dady = -0.072

A: To evaluate the following integral by reversing the order of integration.

Q: 1 14) Find xe™³x² dx . | 0

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Q: Use the law of cosines to determine the length x in each figure. Leave your answers in terms of…

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Q: Given a-6, b-10 and y-120°, use the law of cosines find side c

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Q: Find the radius of convergence for ∞ n=1 n! -xn. 1·3·5· ... · (2n – 1) · (2n – 1) x²

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Q: Verify that (cotx-cscx) (cotx+cscx) + 1 = 0.

A: (cotx-cscx)(cotx+cscx) + 1 = 0.

Q: Use Laplace transforms to solve the initial value problems: 1. y" + 4y= 0; y(0) = 5, y' (0) = 0

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

Q: Solve the following problem and show your complete solutions. Explain your answers for better…

A: given differential equation

Q: To test this series for convergence ∞ Σ n=1 Vn³ +4 n You could use the Limit Comparison Test,…

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Q: 13 Isolate h. 14 Isolate h. Isolate b,. Isolate r & A = = = = (b₁ + b₂) · h V = πr¹h

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Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 7t + 2, y =…

A: Givenx=7t+2..... equation (1)y=3t+9......equation (2)y=f(x)

Q: 1 = f(x) = x + x+7=72₁

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Q: Find the indicated angle 8. (Use either the Law of Sines or the Law of Cosines, as appropriate.…

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Q: Consider the function f defined by the formula [ Ae*-² + cx- 3c f(x) = x³ + cx² + B if x < 2, if x ≥…

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Q: 6) Differentiate: a) y = 2x - x² tanx

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Q: 7. secx dx COS X

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Q: Consider the function f(t) = 9 sec² (t) — 6t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Given, f(t) = 9 sec2(t) - 6t3 F(t) is the antiderivative of f(t) F(0) =0 Find, F(5)

Q: Find the total area of the shaded region. 1.5+ 0.5+ o+ x=y³ 05 x=y² (1.1) X The area is

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Q: Find the indefinite integral. Check your result by differentiating.       −8 dx

A: The objective of this question is to find the indefinite integral of -8 with respect to x and then…

Q: Given a=37, b=32 and c=25, use the law of cosines to find angle y.

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Q: 16. Prove by induction on n that 1 Σi(i+1) i=1 for all positive integers n. n i(i+1) n+1'

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Q: Test the series below for convergence using the Root Test. ) n=1 10n 2n + 1 n The limit of the root…

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Q: To test the series e Find the value of - 4n n=1 the Integral Test. (This is also a geometric series,…

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Q: two linearly independent solutions of the differential equation 3y''-7y'+2y=0 are

A: The given differential equation .The aim is to find the linearly independent solutions of the…

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem for the following function…

A: The objective of this question is to find the value of 'c' that satisfies the Mean Value Theorem for…

Q: What is L(10) C.) When does L=2.5 m?

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Q: Find the given higher-order derivative. f(3)(x) = √√√x8, f(4) (x) ƒ (4)(x) =

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Q: Given the curve تن 2³ + 2xy + y³ = 3 3 Find an equation of the tangent line to the curve at the…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the derivative (a) by evaluating the integral and differentiating the result and (b) by…

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Q: Given a 26° y= 53°, a=9, use the law of sines to find side c.

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Q: 3. Find an equation of the line tangent line to the cure at the point defined and find the value of…

A: As per our guidelines, we are supposed to answer only one question at a time. Since you have posted…

Q: The function f(x) 3x + 6x-1 has one local minimum and one local maximum. Algebraically use the…

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