Find the radius and interval of convergence of the given power series. +o0 (x +3)" Σ 1. n5 +1 n=0 +00 (3x + 4)" 2. Σ n2 n=0

Q: The area which is inside the circle r = 8 cos 0 and outside the circle r = 2 cos 0. %3D

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Q: Consider the points A(1, –1,2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). (a) Find the volume of the...

A: This is a problem related to vector calculation. Please find the procedure given below.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Your factory is going to manufacture a rectangular container which has a fixed capacity V, with a sq...

A: The Volume of a box with a square base  x by xand height  h is V = x2hh=Vx2The amount of material us...

Q: Q3 : Evaluate the following integral. X4V9-x2

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Q: Prove by cases that 25x² + 35x is an even integer whenever 5x-7 is an integer. Note here that the va...

A: Apply the condition for 5x-7 to be an integer case by case. 

Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 s x5 8, 0 s ys V} 29727

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Q: Select ALL possible answers if there is more than one. 1 if x<- 16 2. If f(x) is continuous at x =: ...

A: Differentiable

Q: (a) Oppositely directed to v = (7, –20) and half the length of v. 7 V449 -20 w = 898 8. (b) Length v...

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Q: Evaluate the given integrals. 4. J(secx + tanх)? dx

A: Given problem:- ∫ (tan(x) +sec(x))2 dx   

Q: - Evaluate the following integral. | e2* cos3x dx

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Q: Evaluate the given integral, choose the answer in the box 1/(t-1) 2x S(-1)^5(x-1) -2/(x-1)^2 2/(t-1)...

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, axis and the parabola x2 – 4y – 16...

A: Given:       Parabola x2-4y-16=0                 x2-16=4y                   y=14-x2+16 The area unde...

Q: nclude spaces in between 5. d te In (In y)) at y dy

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Q: Given g(x) ニ X-1

A: We know that, g'(x)=limh→0g(x+h)-g(x)hHere g(x)=1x-1Therefore g(x+h)=1x+h-1Thereforeg'(x)=limh→01x+h...

Q: Three computers are chosen at random from 15 computers of which 5 are defective. Find the probabilit...

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Q: Given a funchion x-2x if x<く2 2-x if x22 Determine if f s cantinuaus at X:72, f yes, find f(X) and f...

A: To solve this problem we will apply the concept of continuity and differentiability of a function at...

Q: 8. 15 Use the figure above to find the exact value of sin 20, cos 20, tan 20. sin 20= cos 20= tan 20...

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Q: B. Directions: Using special functions, evaluate the following:

A: Question 1,Given,           limx→0sinlnx5lnx

Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)², and passing throu...

A: slope m at (2,1)  m = 2(2+5)2 m = 2*49 m = 98 so line equation y - y0 = m(x - x0 ) y -1 = 98(x - 2) ...

Q: O g(x )= ( % x + %); X so , at the point X,=O. x >0 9x - X

A: To check the continuity, we will see the limit of the function at x=0  and the function value at x=0...

Q: 5. Find the Cartesian equation of the plane that has a z-intercept of 3, a y-intercept of -2, and is...

A: Explained below

Q: rtoo Е. re dx स०२२

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Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

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Q: Type your answer in the following order and format: a=0,b=4. DO NOT include spaces in between charac...

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Q: Find f'(x) and f"(x) of f(x) = 11x³.

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Q: Consider the scries > (-1)k (2k + 1)3* k=1 (a) Show that the scries is convergent. (b) Determine how...

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Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

A: We have to find the two unit vectors.

Q: Find the critical numbers, if any, of the function f(x) = 3x5 - 25x3 + 60x + 15 and then use a Maple...

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Q: 2. What is the domain of y = 3x + 2? a. (3, +0) b. (-0, 3) c. (-00, +0) d. (-0,3)(3, -0) 3. What is ...

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = 4x + 7...

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Q: 21,500 %3D C. The cost to maintain inventory for the weather balloons is given by C(x) = where x is ...

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Q: 5. Which of the has a domain of (-o, +c0)? a. f(x) = x b. f(x) = x2 c. f(x) = x d. f(x) = x*

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Q: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

Q: Determine the series of the functions below. Write out the first four terms of the series a) f(x) = ...

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Q: Let a = ci + jand b 8i + 6j. Find c so that the angle between a and bis. Round your answers to four ...

A: Find your answer below 

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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

Q: 5. S(4x+ 2x 1) (12x+ 4x)dr

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Q: 3. At midnight, the heater inside your house breaks down. The temperature (T) inside your house at t...

A: dTdt=-k(T-T0)∫ dT(T-T0)=∫-k dtln(T-T0) =-kt+ln CT=T0 +C e-ktat t=0;T(0)=21°CT0 =-6°C21=-6+CC=27T=T0 ...

Q: Find the area of the triangle with vertices P(1,2, –3), Q(0,0 R(3, 5, 1). NOTE: Enter the exact answ...

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Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: etermine f(x) given that f'(x) = t* – t³ + t2 +t – 1

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Q: A. Directions: Find the limit of the following rational functions: X-1 1. lim x1Vx² + 3 sec x 2. lim...

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Q: Find the nine roots of -256 - j256√3 Give it's exact and approximate value And graph the roots in an...

A: Given expression is: -256-j2563. We have to find nine roots of the expression. 

Q: Use the limit definition in finding/showing what is asked. 2. Given a function x3 – 2x2 if x < 2 if ...

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Q: Find the area of the region enclosed by the parabola y = 2 - x2 and the line y = -x.

A: We have to find the area of the region enclosed by the parabola y = 2 - x2 and the line y = -x.

Q: x2sinx Find dy /dx %3D (1+x2)2V1+x

A: Given: y=x2sinx1+x221+x   We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The...

Q: Q3 : Evaluate the following integral. x+V9-x2 xps

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Q: Jun has decided to save money roughly P25 per week. Suppose he makes weekly deposits of this money i...

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Q: Find the coordinates of the centroid of the solid generated when region bounded by x2 + y? – 4y = 0 ...

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