Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1, 1].

Q: 9-1² 9-1²-² 1.****** (a) 1 dz dy da Sketch each of the following: . the solid E • the projection of…

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Q: Solve the following initial value problem using Laplace transforms. d² y dt² -9y=4e³¹; y (0) = 0,…

A: d2y/dt2 - 9y =4e3t; y(0)=0, y'(0)=-1.

Q: 3. Consider the vectors X and Y in R³ where X = i +3j and Y = 4i - 2j+2k. Find the unit vector…

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Q: Write the given system in the form x' = P(t)x+ f(t). x' = 4x+6y + 8 et y' = 8x-y-t¹ D-AD-41 C

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Q: 9 At what point do the following lines in R³ intersect? h: (x, y, z)=(3, 1, 2) + s(1,0,2), SER 1₂:…

A: Let's find point of intersection.

Q: Based on the graph of the function below, where do the discontinuities of f(x) occur? x = 1, x = -1…

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Q: For the following flux rules, determine regions of the real line where u is instantaneously…

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Q: x" -2x +x= 15; x (0) = 7, x (0) = -16

A: We have solve the given differentiable equation…

Q: ST 5*5*², 5x5x²x² coscyl dy d z d x

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Q: 5. 1-cos2y 1+cos2y dy

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Q: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

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Q: Given w = xe¯ª + ln(x²yz³). Determine δω ?х ?w dx 2 = -xe tết xyz³ dw = xe¯* + 1 + 1²/12 8x dw…

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Q: 4. y +==y² A.-4-2 5. 4x² + 4y2 = 36 A. - 6. x² + 3xy-y = 7 A. 2x-3y 3x-1 B. 3 B. 4y-2 KIA 2x+3y 3x-1…

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Q: Find the marginal profit when (a) x= 300, (b)x=2000, (c) x=6000, and (d) x = 12,000. (a) When x =…

A: Given P(x) = 0.06x ^ 2 - 3x + 7x ^ 0.4 - 5100 P(x) = 0.06x ^ 2 - 3x + 7x ^ 0.4

Q: f(x)= √x-2x √√x X ; f(x)

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Q: x-2x +x= 15; x (0) = 7, x (0) = -16 hand written plz

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Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: Show that the following series is divergent using the Test for Divergence. 4k³ - 1 k³ + 5k² + k k=1

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Q: Question 6c. Consider the region enclosed by the functions f(x) = √√x and g(x) =−x√x+2√x c) Find the…

A: Topic = Area

Q: Given f(x, y, z) = ze™" - a sin none of the choices 02-1/ 02²/ 0 01- ¹(), what is fax (0,2,1)?

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Q: How many asymptotes (both vertical and horizontal) does the following function have: sin(x) -?…

A: To determine the number of asymptotes for the given function.

Q: d.w. Find the lengths for the - r = 1 + cosa

A: Given: r=1+cosθ

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

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

Q: Use Lagrange multipliers z = f(x, y) = x² − xy + y² to find the absolute maximum and minimum values…

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Q: 7 Which of the following functions is not differentiable on all of R? Select one alternative:…

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Q: The speed of sound traveling through ocean water with salinity 35 parts per thousand has been…

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Q: Determine whether the series Σn=1 3n+¹ ln(n+1) is convergent or divergent.

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Please see the below picture for detailed solution.

Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: 29 ² (²4) is the derivative of a function g(x). Over which one of the following intervals is the…

A: Given :g'(x)=x2x2-4x2+1

Q: For the following exercises, draw a typical slice and find the volume using the slicing method for…

A: Follow the procedure given below.

Q: -2 2 о 0 Ау N Х

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Q: ki a) limx→∞ f (x) = b) limx-f(x) = c) limx-of (x) = d) limx-3f(x) =

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Q: Given the graph below, what can you say about the function at x = -2? Not Continuous Continuous

A: A function f(x) is continuous at x=a if and only if limx→a f(x) = f(a).

Q: Create a system of linear equations with three equations and three unknowns, solve the system of…

A: John invested his inheritance of $12,000 in three different funds: part in a money-market fund…

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: According to company's rules, I need to solve first question when multiple questions are posted.. So…

Q: What is the indefinite integral of f (x) = x² + 12? f (x² +12) dx = 3 + 12x + C 1 3x³ S(x² + 12)dx =…

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Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² - x)))

A: Let's find limit of given function.

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. y = x²…

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Q: Question 7a. Zombies have invaded campus! They recruit more of the undead at the rate: dz 10 f(x) =…

A: For Equilibrium value , derivative is zero .

Q: x -2x +x= 15; x (0) = 7, x (0) = -16

A: This question is based on diffrential equation solved using Laplace transform.

Q: The graph of } = xe-r is symmetric with respect to the Origin None of these the x-axis the y-axis

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Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: 1. n² Determine whether the series Σn=13n+1 ln(n+1) is convergent or divergent.

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Q: Determine the intervals over which the function shown below is continuous. Enter your answer in…

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Q: Question 3 Sketch the following function fully: €²-2²-1 y= ²-4 Upload Choose a File

A: Given function, y= (ex-x2-1)/(x2-4)

Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: What is the derivative of y = √/x? 1x² X 2 2 1 X X 2 23

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Q: 41- - ST x² coscyldy dz dx

A: ∫ cos(y) dy= sin(y)+C

Q: _z = g(x,y)=√x² +2y²

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