Predict the general term, or nth term, an, of the sequence. - 12, 36, - 108, 324, - 972, ... an (Simplify your answer.)

Q: Q.1/ Find the area of the region bounded by the line y = 1- x and the curve x = 3 - y2. Q.2/ Change…

A: Area bounded by the curves :  If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y) on…

Q: QS: Find the first derivative at x = 2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057…

A: Solution: Given

Q: メyゴ= ザ+×x。+y %3D ind gen eral solution

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Q: Step 4 tan-(8x), then converting back to an expression in x we get u2 + C = 16

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Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) а. Find the…

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Q: Find the Maclaurin series of f(x) = 14 cos (-x). %3D What is the Maclaurin series of 14 cos (-x)? 00…

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Q: Find the derivative of the given function. dx %3D

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Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: Find the limit. Use l'Hospital's rule if appropriate. If there is a more elementary method, consider…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Describe the graph of the equation: r = 34 – Sj + (I + 30k. [Choose the correct answer) O The…

A: Given problem:-

Q: Given: f(x, y) = 2xy; R is bounded by x = 8, y = 0, and y = x Question: What is the double integral…

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Q: tan The integral -dx is equal to ONE of the following. (HINT: Use Maclaurin series) (-1)" ó 2"+'(2n+…

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Q: Given A = (-5, – 3) and B= (2,6), determine: a) AB b) AB

A: Given :A=(-5,-3)B=(2,6)

Q: For the given functions, find (fo g)(x) and (go f)(x) and the domain of each. 1(x) = 9(x) = 1-8x

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Q: 2. Let R(t) = sin 4t î – bcos"(21) j + 2t k. Find the moving %3D trihedral of the curve of R(t) at…

A: Given

Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: A rectangular box with an open top is to be made from a 9-inch by 24-inch piece of cardboard by…

A: This question is based on application of derivative.

Q: Let F(x) = f(x*) and G(x) = (f(x))* . You also know that a? 5, f(a) = 3, f'(a) = 3, f'(a*) = 9 %3D…

A: Given that,F(x)=fx3 and Gx=fx3

Q: A rancher has 300 feet of fencing to enclose two adjacent rectangular corrals, as shown in the…

A: Maximize area

Q: 12. Find all relative extrema, and sketch the graph, for the function: f(x) = 3x* – 4x -12x² %3D…

A: Given

Q: A region is enclosed by the equations below. y = cos(3z), y = 0, x = 0 6 Find the volume of the…

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Q: given funchiow: fox) = x?e?" Defermine any pants of inflectro

A: Given :f(x)=x2e7x

Q: Find the length of the curve y = xVa 0 <x < 1.

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Q: x3 Evaluate J (3-2x) using substitution

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Q: Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by: (vi, v2) O (W1, w2) :=…

A: The objective of the question is computing the values.

Q: We must also convert dx into an expression involving u. We know that du dx, and so x3 dx = X du.

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Q: 1. The position of a particle is given by the function s(t) = t* – 32t where t is measured in…

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Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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Q: Find a gradient of the equation: F(x,y) = v2x + :- y sin a + 4 VF =?

A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

Q: 2. Write the given (total) area as an integral a. The area above the x axis and below y = 4-x2 Ne -…

A: Since, the student has mentioned to solve only question number 2, so we are solving accordingly only…

Q: 23. cos (3z + 4) dz 25. sec2 (3x + 2) dx

A: A

Q: Find the equation which satisfies the separable differential equation dy – 15x dx with the initial…

A: Given dydx=-15xy    y(1)=-5To find solution:

Q: Suppose that f(x)=2x^−4+5x^−2 Evaluate each of the following: 1. F' (2)= 2. F' (-1)=

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Q: Ballast Dropped from a Balloon A ballast is dropped from a stationary hot-air balloon that is…

A: Given query is to find the height of the blast after t time and the time when it will hit the…

Q: Find y subject to the given conditions. y"= 12x, y"(0) = 14, y'(0) = 4, and y(0) = 4

A: To find y subject to given conditions.

Q: Q 25-The Laplace transform of function f(t) = e¯'sinh4t is a) 2/(s²+2s) b) 2/(s²+2s+15) Q?-The…

A: To Find : laplace transform of f(t)=e-tsinh(4t)

Q: Find the indefinite integral. Hint: Let u = 5- Vx. (Remember the constant of integration. Remember…

A: To evaluate the given intgral.

Q: Determine which value best approximates the surface area of z = f(x, y) over the region R. (Make…

A: Given that the area of surface z = f(x,y) over the region. Let consider the given function, f(x,y) =…

Q: The following data lists different investment amounts (X) and the amount of interest (Y): X5 Y 2.5…

A: Here is the solution:

Q: a) Determine the position function, s(t), of an object if the acceleration is a(t) = 3t , v(2) = 0,…

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Q: Find the partial sum for the firs 4, 10, 16, 22, ... い +6 +6

A: Sequence

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

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Q: n(x-3)" Find the series' radius and interval of convergence Zn=1 2n /n2+1 100 Paragraph B IU A Lato…

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Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

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Q: Given the functions f(x) = . x + 2 and g(x) = x², determine all values of x for which Ag(x)) =…

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Q: Find the derivative y = 2 Arcsin 2 -2 a. y' = b. y' = c. y' = d. y' = V2x-x² V2x-x2 V2x-x? 2x-x²

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Q: 15 If f(x) 2 sin : then f'(x)

A: We will find f'(x) of the given function f(x)=2sin-1x5 in the following step.

Q: 3) Verify that the hypotheses of Rolle's Theorem are satisfied on the given interval, and find all…

A: Solve the following

Q: For the given cost function C(x) 22500 + 600x + x², First, find the average cost function. Use it to…

A: For the given cost function Cx=22500+600x+x2, First, to find the average cost function. Then by…

Q: Find the general solution of the second-order differential equation: 4y" – 4y' + 13y = 0.

A: To find the general solution of given differential equation