₁+∞ n(3x + 2)n n³ + 4 Given the power series Prove that the series is absolutely convergent when x = 1. Solve for the interval of convergence. ● n=1

Q: Write 0.12 as a fraction. Use the concepts in section 10.3

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Q: If two terms of an arithmetic sequence are a₁₁ = 26 and 815 = -10, what is 828? -226 O-217 O-127…

A: I have stated the used formula in the solution.

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Q: Differentiate y = (2x³ + 3x² - 1)5 5(6x² +6x)4 30x(x+1)(2x³ + 3x² - 1)4 30x(x + 1)(2x³ + 3x²-1) O…

A: The given function y=2x3+3x2-15 we have to find the derivative of the function

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Q: If what does the following integral equal? [q(w)dw = [ [²³q(w)dw = 12 and q(w)dw = 9.4 1. 2

A: This question can be solved using the concept of definite integrals.

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A: Topic:- trigonometry

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Q: Which term is -708,588 for the following sequence, assuming that the pattern continues? 4, -12, 36,…

A: Solving the problem by finding the value of the n-th term .

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A: Find domain & range

Q: IV. Fill in the blank to make each statement true. Use correct notations. ¹(si 1. sin-1 sin 12πT 5…

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Q: 2. Sketch the solution region of 2x - y - 1>0 (x - 5)² + (y + 1)² ≤ 25.

A: The given inequalities, 2x-y-1>0(x-5)2+(y+1)2≤25

Q: Supply function is defined as

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Q: Evaluate the following indefinite integral. 1 √ 3 ² + 8 - t dt =

A: Given.

Q: Find the breakeven point of the following functions: C(x) = 5x - 7 R(x) = 2x Approximately (2,…

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Q: 3. S (5y-4)dy y³+4y²

A: We know, ∫dx/x= ln|x|

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A: Here we have to find the value of x.

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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Q: Consider the graph y = f(x) below. -4 -3 -2 3 2 tion 8 6 2 3 T Find all value(s) of a such that lim…

A: The objective of the question is determine the points in which limits doesn't exist and not…

Q: What is the domain of the rational function(x)=-3x²-16x +48 Oxe 31x*-4,-2.3.4) Oxe 31x*-4, 3, 4) O…

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Q: 5. Given that f(t) = sint, t=0, t≥π/2 0≤t<π/2 find L{f(t)}.

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Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: (27 - ㅎ) (2급 + 글 이효리 17 U O 112-10 U 4u 4 u - 2 U 2 2

A: Topic:- application of vector algebra

Q: 5. What is odd and even function?

A: We have to define odd and even function.

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

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A: Given that f(x)=1-log5 x , then our aim is to find the value of f-1 (x)=?

Q: price

A: At Equilibrium, Demand = Supply,

Q: A student was asked to determine the y-intercept for the logarithmic function f(x) = log₂(x + 3) +…

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Q: Determine the slope of the tangent for: Y = ㅇ- O 0 을 -100 2+5 √ã at : (4, 을)

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Q: If ¹f [ 2³ sin ædæ = −2³ cos x + 3x² sin æ+ 6x cos a - 6 [ f(x)dæ, then f(x) = a. x cos x b. sin x…

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Q: Find the minimum value of the parabola using the following equation: f(x)=1/4(x+4)^2 +3 y = 4…

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Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: This question can be solved using the concept of maxima and minima.

Q: Which of the following graphs represents (x + 1)² = 8(y - 3)?

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Q: Determine the interval of convergence of n=1 (x - 5)" n²

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Q: Shoppers at Pageturner's Bookstore are tracked, with the following results: 34% visit the…

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Q: Find all solutions in the interval [0,4π) Give solutions accurate to 5 decimal places. b)…

A: We need to solve for x.

Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: The graph will be  Option (B)

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A: Let P be the population,t be the time and k be the growth constant. We know that exponential growth…

Q: 1/3 0 4x dx √25-x

A: Given Problem:- ∫0134x25-x4dx

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Q: e) lim (1+sec 3x)cot 3x 7 2 X-

A: The objective is to find the limit.

Q: Evaluate ff (2x+5y+z) ds (2x+5y+z) ds where the surface S is given by S S: z=15-2x+3y, 0≤x≤1, 0≤y≤2.

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Q: Determine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: This exercise uses the radioactive decay model.. The half-life of radium-226 is 1600 years. Suppose…

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Q: dt 1²+8t+20

A: We can find the answer as below.

Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: Find the volume of a solid obtained by rotating the region enclosed by the graphs y = 19 - 2x, y =…

A: To find the volume of a solid obtained by rotating the region enclosed by the graphs y=19-2x, y=5,…