Trigonometric Substitution SV9-y dy Vy dx 6. S e 2x+1

Q: -1)" =£ Given: In(1 + x) if x < 1. n + 1 n=0 (-1)" (n +2 2n+1(n + 1) 4. Compute the exact value of…

A: ln(1+x)=∑n=0∞(-1)nn+1xn+1     if x&lt;111-x=∑n=0∞xn  if x&lt;1

Q: Let /(x)= 5+ 6x Compute f(1) S'(1) s"(1) s"(1) sim(1) = sm(1) We see that the first term does not…

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Q: COuld I please have help with the third multiple choice question? Thank you.

A: We have to find the conclusion.

Q: dy 3.The differential equation = xy – y+ x is separable. da A. False о в. True

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Q: Write the partial fraction decomposition of the improper rational expression. x4 + 2x3 + 8x² + 13x +…

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Q: 10. Find the average value of the function f (x) x + Vx %D on the interval xe[0,8]. Graph on Desmos.

A: Given problem:- Find the average value of the function f(x)=(1/2)x+x(1/3) on the interval xe [0,8].…

Q: Find the absolute maximum value of f(æ) = [0, 5] x2 – 2x + 12 over the interval

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Q: Two parametric equations are given by: x = cos (t), y = sin³(t) u = sin(t) , v = cos(t) In one…

A: Let's find.

Q: Evaluate the integral using the following values. 8. 8. x dx = 960, х dx %3D 24, 8. dx = 4 4 х dx 4

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Q: Find the open intervals where the function is concave upward or concave downward. Find any…

A: Here, the given function is: f(x)=-2x2-4x+2

Q: 3 | (16t³ – 9t² + 7)dt Evaluate:

A: Given problem:-

Q: Direction: Evaluate the following functions. Show the step by step process by using the limit laws.…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Graph the function and find its average value over the given interval а. g(x) %3D \x| —1 оп [-1,1]…

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Q: Plot the polar point ( -4, 165° )

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Q: What is the total interest earned, including compound interest, if you left $500 in a savings…

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Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: Find a power series representation for the function. (Give your power series representation centered…

A: We will use binomial theorem for the expansion of the function.

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   g(x, y) =…

Q: The nght-circular conical tank shown in Figure 6.2 below leaks water out of a circular hole at its…

A: answer is in next step

Q: If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height (in meters)…

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Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

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Q: Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) =…

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Q: 1. Solve x+2|<6

A: Topic = Inequality As per guidelines , At a time only one question  can be answered out of multiple…

Q: Let {an}, be a sequence of real numbers. Let a2k and a2k–1 be the even and odd terms of this…

A: We have to prove that sequence an converge to L.

Q: 2r? xp : Vi – 4x³

A: The objective of the question is evaluate the indefinite integral.

Q: Activity 1.3.3. A water balloon is tossed vertically in the air from a window. The balloon's height…

A: Given problem:- A water balloon is tossed vertically in the air from a window. The balloon's height…

Q: 10. Find the average value of the function f (x) 1 = -x + Vx on the interval xe[0,8]. Graph on…

A: The average value of the function is given by;favg =1b-a ∫abf(x) dxTo plot the average function…

Q: Find dy/dx: a. y = cos t dt 0,

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

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Given: As no method is mentioned, we will be answering by graphical method.

Q: Evaluate the Following limts 9-X VX-3

A: We can evaluate the limit as below.

Q: 12 10 12 | f(æ) dæ = 9, | f(x) da = 14, | f(x) dz = 5. Suppoe 6. 11 Then 11 | f(x) dx = Σ %3D 10 10…

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Q: N(N+1) N(N+1)(2N+1) N (N+1)? Use linearity and the formulas Ej = E = and Σ"- to evaluate the sum. 4…

A: ∑j=0 46j(j-1)=∑j=0 46 j2-j=∑j=0 46 j2-j  =∑j=0 46 j2-∑j=0 46 j

Q: 2) y = 3tan 3 - -2 3n 27 5n 3n 7 47 9n

A: Given query is to graph the function.

Q: Find dy/dx: y = cos t dt = | Vũ du b. у y = -sin x = 3t² dt с. y = tan x d. y = | sec? t dt 0, 3 dx…

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

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Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Eva luate the Following limits 2) lim x-74 X2-X-12 *-1 s.) limx->4 *2+x=2

A: To evaluate the following limits.2 limx→4 x2-x-12x2-x-203 limx→1 x-1x2+x-2

Q: V3x+1(4x+1) (1– 2x)* Calculate y: y=

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Q: I Find tee e avation of tangent line of fcx) = X+) at X=2 X-3

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Q: Problem 6. The following series are geometric series. Determine whether each series converges or…

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Q: Find the absolute maximum value of f(x) = x² – 2x + 8 over the interval [0,5|

A: The objective of the question is determine the absolute maximum value of the given function.

Q: Evaluate the tolloW ing limits と-1

A: =limx→1  x-1x2+x-2=limx→1  x-1x2+2x-x-2=limx→1  x-1x(x+2)-(x+2)=limx→1  x-1(x+2)(x-1)=limx→1…

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: 2. Suppose that f(x) is a function with f(20) = 345 and f'(20)=6. Estimate f(22). [4 marks]

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Q: x*-y* 3) x²y³ = **-y+ ху

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Q: Evaluate the integral. 1 | (4 + r)³ dr

A: Given query is to find the value of the integral.

Q: dz Find dt(t=1,s=0) when z = 2x3 + 15y3, where x = t2 - s and y =t+ 2s2

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Q: . The population of a bacteria colony after t hours is given by P(() = 2000e growth rate of the…

A: To determine the growth rate of colony at given time.

Q: 2. Write z = -ói in polar form. O z = 6cis= 2 O z = 6cis- Oz =-6cis- 2 Oz = 6/2 cis 37 2 3. Write z=…

A: Let, z= 6 (cos(π/2) +isin(π/2))  or, z=6cis(π/2)