Use the Limit Comparison Test to determine the convergence or divergence of the series. lim 818 00 n = 1 6 7 + 1 + 1 6 +1 7 +1 O converges Odiverges =L>0

Q: Which of the following conditions will make the equation equation of a sphere in xyz-space Oa>b>c…

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Q: The ellipse 13x² + 2x + y² = 1 has its center at the point (h, k) where h= The length of the major…

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Q: e area under the given curve over the indicated interval. 8) y = 7; [2, 9] 8- 7- S 4+ 3+ 2+ 1 A) 14…

A: Given query is to find the area of the curve.

Q: a. Determine whether the Mean Value Theorem applies to the function f(x) = ex on the given interval…

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Q: Find the Maclaurin series for f(x) = cos(19x). cos(19x) = Σ n0

A: As we know that: Maclaurin series for the cosx centered at x=0 is given by f(x)=∑k=0∞(-1)kx2k(2k)!…

Q: 3. Set up an integral (do not evaluate) that represents the area of the region that lies inside the…

A: We have to set up the integral to find the area.

Q: Given the sequence 41, 4.4 what is f(n)? 4+ f(n)=4+ f(n)=n+ f(n)-5-- 4+n 1 4+n n

A: We rae required to find the general term of the given sequence.

Q: ing or decreasing.

A: We have to find the following conditions according to the given information

Q: 2. Consider the parametric equations x = 3 sin (t) and y = 3 cos (t) (a) Determine dy/dx in terms of…

A: We need to find derivative.

Q: Perform a first derivative test on the function f(x) = 2x³ + 6x² - 48x+6; [-4,6]. a. Locate the…

A: From given function we have to find the value of vritical points. We also find local minima and…

Q: 9. Find the area of the lateral surface of the cone of radius 4, height 9, obtained by reloving the…

A: To find the lateral surface area of the cone of radius 4, height 9, obtained by revolving the curve…

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 4t,…

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Q: A 7ft ladder leans against the side of a house. How far is the bottom of the ladder form the side of…

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Q: Find a formula for the inverse of the function. g(x) = x² - 4x, x ≥ 2 g-¹(x) = 2+√√-1(-4-x),x≥-4 ×

A: Given that , gx=x2-4x   ,    x≥2 find the inverse of the function.

Q: Solve the following differential equation by separating variables and solving for the EXPLICIT…

A: Given query is to find the solution of the differential equation.

Q: Evaluate the integral: f t² sec² t³ (tan t³ - 1)² -dt

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Q: A manager at the Black Box microprocessor manufacturing company finds through data gathered in…

A: we need to find the cost function and fixed costs.

Q: P3 Find the Maclaurin expansion for the following functions and indicate for which values of a it…

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Q: Show the solution : S (sinx + cos x) dx sin²x answer: -In /cotx + cscxl-cs

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Q: What interest is accumulated on an investment of $10,000 left in a bank for  5 years with an…

A: use the simple interest formula for calculating the interest.

Q: Represent the function as a power series f(x) = ²n 9x 9 + x Cnxn CO 5 C1 || C2 C3 = -9 || 1 h -1 C4…

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Q: Find the first four nonzero terms of the binomial series for (1+x²)71/³

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Q: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) f(x) =…

A: We have to slove above questions

Q: A rectangular swimming pool 40 ft long, 30 ft wide, and 12 ft deep is filled with water to a depth…

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Q: dy dx 11 1 x log x

A: ∫1xdx=lnx+cdlogxdx=1xdydx=1xlogxdy=1xlogxdxintegrate both side

Q: 4. Find the formula for the inverse function of f(x): f^(-1)(x) 3x - 5 4x + 1 ƒ(x) = =

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Q: +5 ο 2 -2. 7=1 4" n (2n)! 4/(1+1), (6(+1) ( 2 (n+1))! 4/20 (zn)! 2ntit. 1:m 1700 hod 2ntl linn (1)…

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Q: Select all that the derivative represents. Select 3 correct answer(s) The slope of the tangent line.…

A: The objective of the question is choose the correct option for derivative represents.

Q: Determine whether Rolle's theorem applies to the function shown below on the given interval. If so,…

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Q: You receive two job offers: Job A: $41,000 starting salary, with 6% annual raises Job B: $52,000…

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Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 5 Σ n=1…

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Q: Evaluate the definite integral D = r/2 D = = ST cos(2 w) dw. NOTE: Use exact values only. Do not…

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Q: Find the critical points of the following function. f(x) = 2x²-3x - 4 Select the correct choice…

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Q: Differentiate implicitly to find d2y/dx2.   x3-y3=12

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Q: 10. Determine whether the following series converge or diverge: (Integral Test) a) En=2 In (n) n 1…

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Q: 1. Evaluate the double integral (2² IMO (2²+2y) dA where D is the region bounded by y = z, y = r³,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Evaluate the surface integral. JY y ds, S is the helicoid with vector equation r(u, v) = (u cos(v),…

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Q: 8. g(x) = n(1+t²)dt 12. R(y) = t³ sin(t)dt

A: To find the derivative of the following functions.8 gx=∫1x ln1+t2 dt12 Ry=∫y2t3 sint dt

Q: Use the method of partial fractions to evaluate: 3x + 10 x² + 9x + 20 2 S dx

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Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A: We need to perform left endpoint approximation.

Q: 35. For m = (-5, -6) and = (6, −9) find the sum of the vector three times the magnitude of m and the…

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Q: 5. Graph 0= 2T 3

A: Please see the below picture for detailed solution.

Q: Consider (A) What are the equilibrium solutions? the initial value problem given by: d = x² (4 − y)…

A: A)  for equilibrium solutions put dydx=0∫xndx=xn+1n+1+c

Q: (a) 63°

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

Q: 1. Evaluate the following integral or state that it diverges: a) So dx (1+x) √x 2dx b) ² 24 +4 c) f%…

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Q: 33. The graph of f is shown. Evaluate each integral by inter- preting it in terms of areas. (a)…

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Q: (a) Estimate the area under the graph of the function f(x) = endpoints. Round your answer to four…

A: Let's find area under the curve  by using right and left endpoints.

Q: A tank contains 500 m³ of solution with 12 kg of dissolved chloride. A water enters the tank at rate…

A: Let's find amount of salt in the tank after 5 minutes.

Q: Question Given the point (6, form. 70 in polar coordinates, find the rectangular coordinates of the…

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Q: 1. Convert each of the following radians to degrees and sketch the angle measure: a. π/6 b. π/4 C.…

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