Evaluate the definite integral (12a² – 6x + 6)dx 3.

Q: Find the area bounded by the curve y = 4x-x and and the lines x = 0 and y = 4. %3D Answer.

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Q: A. For the following power series determine the interval and radius of n+1 convergence.a (x - 2)"…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Consider the function f(x) — 6ӕ* — 9a? + 10х — 9. - An antiderivative of f(x) is F(x) = Ax* + Bx³ +…

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Q: Three forces are simultaneously acting on an object. The first force is 1200 N downward, the second…

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Q: | cos ) sin(x) dx

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Q: power series converges at a single a. what is the radius Of ConvergCnC (c) R=0

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Q: The series 32n-54-1 -2n is n=1 Select one: O a. is a divergent geometric series. O b. is divergent…

A: This question can be solved using the concept of ratio test for convergence and divergence.

Q: 24. Solve the system. [x, y] = [-9, – 1] + s{2,3] [x, y) = [-8,2) + 1{2.1]

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Q: 1. Lets say Q(x) = 5x + 2 P(x) = 3x2 - 5x +1 %3D Find (a) Q (-3) (b) P(5) (c) 5P(x) – 2Q(x) (d)…

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Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

Q: - the solution of the following O.D.E y' = cos(x) +y

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the Demand Function D(p)= 275-4p^2 Find the Elasticity of Demand at a price of $5

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Q: Consider the function f(x) = 2x – 6x² – 48x + 1 on the interval [– 6, 8]. Find the average or mean…

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Q: How did you get the expression for xtan^-1(x)? How did you relate it with the maclaurin series of…

A: Apologies for the inconvenience. Here is the correct solution.    Given that:…

Q: Find an equation of the parabola whose graph is shown. y WebAssign Plot (49, -7)

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/ō-definition of the derivative to prove that f(2) =9.

A: given :f(x)=4x2-7x

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given ,  Two cars are initially 1200 miles apart  At the same time Car A starts driving at 35 mph to…

Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: 2. Let R(t) = } sin 4t î – bcos“(21) j + 2t k. E

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Q: Find the parameter k such that the function y cos(kx) satisfies the equation y + 5y" = 0.

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Q: Find the average value of the function f(t) = 4 t sine) on the interval [0, 20]. Round your answer…

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Q: Problem 2: Given a function 4x -1 f(x) = 2x +1 Use tabular method to determine if the limit of a…

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Q: 3. A rectangle is inscribed under the curve of f(x) = e-*², where one side of the rectangle lies on…

A: Follow the procedure given below.

Q: Find the limit. Show all work. Vx +5 -3 1. lim- 2x? –x-3 COSX 2. lim X--1 3. lim x-/2 Cotx X4 X- 4…

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Q: Use a graph to determine whether the given function is continuous on its domain. [3 – x if x 3…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) sec t (8 sect + 9 tan…

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 7. 1. A = 4 6. 4…

A: 1.A=7-346 det(A)=7×6-(-3)×4=42+12=54 2.B=4-5-19 det(B)=4×9-(-5)×(-1)=36-5=31 3.C=213-312-27…

Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = (x – 5)3 g(x) = x - 5 y 1.5| 1.0…

A: This question can be solved using the concept of area under curves.

Q: Only pose the triple integral that calculates the volume of the solid bounded by the surface y2…

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Q: Find the equation of the tangent line to the graph of the given equation at the specified point. y =…

A: We can find the equation of tangent line as below.

Q: 2x)y'+5y=

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Q: Find the volume of the solid obtained by rotating the region bounded by the curves y = x°, y = 1

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Q: 49 x dx -7

A: answer is in next step

Q: Use the direct comparison test to determine if the following series converges or diverges. sin?n Σ…

A: Solve the following

Q: 2/11 Correct Question 4 of 11, Step 1 of 1 2 Consider the function f(x) = x - 6x - 4 on the interval…

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Q: Find the Taylor series generated by f at x = a. 1 f (x) a =3 4-x

A: Solve the following

Q: For the function y f(x) - la + 10: - df at x = 1. dx a. Find f'(1) = b. Find a formula for x =…

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Q: (b) А — В (с) 2A (d) 2A – 5B

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Q: 6. Let 4-x? < f(x)< 4 + x². Use the sandwich theorem to determine the limf(x). Show all work!

A: Use sandwich theorem

Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

Q: 2. Let f (x) = 3 cos(2x) – 1. (a) Find the period and the amplitude. (b) Sketch the graph of the…

A: Use function

Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

A: Draw the diagram and use the washer method of finding volume of rotation.

Q: Liquid leaked from a damaged tank at a rate of r(t) liters per hour. The rate decreased as time…

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Q: 10* dx (10*+1)5

A: We can solve the integration as below.

Q: y=f(x) A1 АЗ 15 A2 7 A4 10 (figure is NOT to scale) Evaluate the integral below by interpreting it…

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Q: What is the slope of the tangent to the curve y=arctan 4x at x= 1/4 A. -2 B. 0 C. 1/2 D. 2…

A: To find the slope of tangent to the given curve.

Q: Find the center of mass for the following masses along the x-axis (distances are in cm): 42g at…

A: Center of mass = sumation of mi xi / summation of mi

Q: How to find point of intersection?

A: You have to sketch the graphs using a graphing calculator like this:

Q: Give the generator, the directrix, and the rulings of the cylinder x = lnz. Draw a sketch of the…

A: We need to give generator, the directrix, and the rulings of the cylinder x = lnz.