Determine whether the series converges or diverges. In(k) k k = 1 converges diverges

Q: Graph the following function. Then estimate any relative extrema. (x) = x° (2 - 3x)3 Choose the corr...

A: Given that fx=x2 2-3x3Solution if we have to find relative extremum then f'x=0 and solve . if f'x +v...

Q: Differential equation A tank initially contains 10 gal of fresh water. At t= 0, a tap is opened, po...

A: Given

Q: 5. Use the integral test to determine the values of p for which the series below will converge. 1 k(...

A: Here we have to use the integral test to determine the value of p for which the series below will co...

Q: Find $Y if y = x-3 x -7 ond X=2++1 %3D

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Q: Consider the function f(x) whose graph is given below. y= f(x) in Enumerate all discontinuities of f...

A: Here f(x) is not defined but at x=-2, x=3, x=5 .

Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or...

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Q: Find the limits of the Follo CoS \im

A: Given query is to find the limit of the expression.

Q: 3 8. If sin e = - - and the terminal side of e lies in quadrant III, find cos e. 5 3 3

A: Topic  = Trigonometric ratios

Q: Question 2 Let D1 be the solid in space that lies in the first octant x, y, z > 0, and be- tween the...

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Q: The school director of Saint Louis School of Pacdal, Inc, wants to construct a rectangulr wants to b...

A: To find: The dimensions of the garden to be maximized: Given information: The school director wants ...

Q: X+イ

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Q: ()" e n n=0

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Q: Given f''(x)=−9sin(3x) and f'(0)=4 and f(0)=−1.   Find f(π/4)=

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Q: Compute T (æ) at a = 0.9 for y = e" and use a calculator to compute the error le – T2(x)| at a = 0.5...

A: Find your answer below 

Q: 3. When a camera flashes, the intensity of light seen by the eye is given by the function: 100t I(t)...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Find the critical point(s) of the function f(x, y) = 6x²y – 12a2 – 3y? and use the second derivative...

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Q: By completing the square, dx the integral S is equal to: (x+5)Vx²+10x+21

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Q: Integrate S (a?- ) dv ; where " a" is constant O = - + C 3 =-{ (a? – v²)* + (a? – v²)* + C O = (2? –...

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Q: Let S be the region enclosed by the graphs of y = 2x and y = 2x² for [0,1]. What is the volume of th...

A: We have to find the volume of the solid.

Q: If a force of 60 lb. acts at an angle of 40 to the horizontal, what is its vertical component? 39 l...

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Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

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Q: A taxi company charges for rides according to the following. The cost for every ride starts at $3.50...

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Q: 2. Find Y if y =x +3x-7 and x 21 +1.

A: Given: y=x2+3x-7x=2t+1  

Q: Activity 3.3. Find the equation of the tangent line to the curve f at the given value of x. Show and...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about r = r, and then find the nth Taylo...

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Q: 1 1 cos³30 \cos830) sin330

A: Solution is written in below steps.

Q: The graph of a function f is shown below. x3 x4 x5 x2 At which of the labeled r-values is f(x) least...

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Q: A. True or False. Write T if the statement is TRUE, otherwise write F. 1. The function f(x) = discon...

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Q: c) an (-1)" (4)" d) аn — 5 — п

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Q: Order the functions from slowest growing to fastest growing as x -o: 4x², (In x)³, 10*, and e2x

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Q: c) Determine if y=x tan (x) satisfy dy _ y _ y sec?(r) = 0 when yLu-0=0

A: Put value in equation for satisfied

Q: Solve the inequality - 2 3 and enter your solution set in the box below using interval notation. To ...

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Q: 3. Find from the following functions: dx y = (12x + 2)(7x + 3)3/2 18+2x+7 y = (i) (ii) (3x+6)2/3

A: 3)I) y=(12x+2)(7x+3)3/2 ii)y=(18x2+2x+7)/(3x+6)2/3.

Q: find as xm Plotes of the following carre then graß h them X-4

A: Given query is to find the asymptotes and the graph of the curve 

Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

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Q: 12 ソ+) X +20 x + 20 y+30 1. 1.

A: 1/12 = 1/(x+20) + 1/(y+80) 1/5 = 1/(x+20)  + 1/(y+30) now 1/12 = 1/(x+20) + 1/(y+80) in this  1/(x+2...

Q: Q: solve the equation 5 lim ( 3y+ 4x (37+*-) – x-3 x - 3

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Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is t...

A: Given query is to find the rate of change of area.

Q: inconclusive, then say so. 5* Σ 00 If p = + 0, enter "inty". i The series converges. The series dive...

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Q: Question * The derivative of the function y = x(tan¬1(3x))² is:

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Q: (y-2)(y²+4) 4. S x3-x2+1 dx (x²+2x+2)2

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Q: The graph of f(z) is given by {-1.4) (1, 4) (-1, –2) (5,-2) (3,-4) (-4, 5) Determine if f is continu...

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Q: Find all solutions to the equation |5-3x| -2 +x = 2x + 5

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Q: Find the volume of the solid obtained by rotating the region petween the curves y = 3x - x³ and x-ax...

A: Given query is to find the volume of the solid generated.

Q: Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1<x<1.

A: We have to prove maclaurin series.

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 2(-1)*+1_k+ 10...

A:   ak =(-1)k+1 k+10k(k+11) {bk} =k+10k(k+11)bk - bk+1 =k+10k(k+11)-k+11(k+1)(k+12)=k3+23k2+142k+120-k...

Q: Using integration by parts and taking a > 0, the integral S x In(ax)dx is equal to:

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Q: VI. Give the Maclaurin series expansion of f(r) = In(2 - 3). Determine its interval of convergence. ...

A: This is a problem related to expansion of the given function. By using taylor series at 0 point we w...