(Write the answer in your own handwriting, scan and then upload the file) Q1. Prove that V = (y - z² +3yz – 2x) i +(3xz+ 2.xy) j + (3.xy – 2xz + 2=)k is both solenoidal and irrotational.

Q: e(2e" – 1)dx 6x 3x A 2e - 1 B 2e 6i – e 3u © (e"-2)+ (e" + 1)4 E F None

A: This is a problem of integration. First here we will assume e^3x = t and then we will use general fo...

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Q: e^x Evaluate A arc sin e^x +c B arc tan e^x+ C arc cot e^x+ C

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Q: 100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the ro...

A: Theorem : If the series ∑n=1∞|an| converges, then the series ∑n=1∞an also converges.                ...

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A: area and right end sum

Q: Consider the following functions. f(x) g(x) = 3x + 9 Find (fo g)(x). Find the domain of (fo g)(x). (...

A: Here f(x)=2/x and g(x)=3x+9 (1) (fog)(x)=f(g(x))              =f(3x+9)              =2/(3x+9) The fu...

Q: Direction: I. Determine whether the series converges using any appropriate test. Identify the test f...

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Q: QI/Correct the following items, enhance your answer with a mathematical proof for each item. 1- cosh...

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Q: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

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Q: (b) Then do the following: • If your answer is porsible, provide a specific example (a specific an) ...

A: D. Possible.     ex. an= 1n2  ⊙   limn→∞ 1n2 = 0 . Hence, an  converges.  ⊙  ∑n=1∞1n2 is converges b...

Q: 4" – 3" 00 Determine whether the series converges or diverges. If it converges, find its sum. n= 0

A: Solution: ∑n=0∞4n-3n5n Apply series ratio test an+1an=4n+1-3n+15n+14n-3n5n

Q: If f(x) = 9a'm(z), find f'(9).

A: This is a basic differentiation problem

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y, z) = 2x + 2y...

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Q: 7–√7

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Q: dy Given that y = x² log2(6 – 5x), find dx

A: This question can be solved using product rule of derivative.

Q: 24. Maximizing Area A wire 10 cm long is cut into two pieces, one of lengtn other of length 10 - x, ...

A: First of all we need to find the function for total area of squares. Then for minimizing need to fin...

Q: Find the area of the given region using any method. 1 y = 9 - x2 y 1.5 1.0 0.5 -1 1 -0.5

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Q: [1 23 A 3 4 5] Given matrix A above, in the matrix multiplication: IxA = A.What is matrix To create ...

A: Find your answer below 

Q: a*dy= +C Ina A True (B) False

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Q: sec-dx 3 - 3 In sec – + tan- + C | 3

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Q: a4 a*dy= +C Ina A True B False

A: topic - indefinite integral

Q: Evaluate dw using the given information. 5x? + 4y? w = -; x= - 5, y= 3, z = 1, dx= 0.01, dy = - 0.08...

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Q: G. Find the derivative of the following functions using the limit definition. 1. g(t) = 2-5t 5t+2 2....

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Q: f(x) = 3x + 8 f(x) = - 2 *= 2 f(x) = -x? + 3x +9 x= -6

A: As per our guideline we are supposed to be answer only three subpart of question you can repost othe...

Q: Detemine the x- values at which, g(x)= 2x-3x²+x 2x3+5x²-3x is undepined. Evaluate the limit ac x=8 u...

A: To find: The value of x at which g(x)=2x3-3x2+x2x3+5x2-3x is undefined also evaluate the limit as x=...

Q: A scientist initially has 40 mg of a radioactive compound that decays by about 10% each year (ie. af...

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y) = y² – x² sub...

A: Let's find. 

Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

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Q: Test the series below for convergence using the Ratio Test. 3" п! The limit of the ratio test simpli...

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Q: (secx-2) *dx cosx cotx A cosx cotx B secx -2 C) (secx -2)5 None

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Q: Use a linear approximation (or differentials) to estimate the given number. e0.01

A: We use linear approximation to find e0.01 By linear approximation f(x)=f(a)+f'(a)(x-a) we take a=0 b...

Q: Given f(x) = ln(4 −3x) + 1 state the domain, range, vertical asymptote, end behavior, and x and y-in...

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Q: dy Given y = u? - 1 and x = u2 + 1, find dx

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Q: 2- x*y' y + xy' = 1 3D1

A: Given:        -x2y2y'+xy3=1

Q: Make a conjecture about the derivative by calculating the first few derivatives and observing the re...

A: Here, to make a conjecture about the derivative by calculating the first few derivatives. ddx(sin x)...

Q: a) The value of the following integral 224 2da is Answer: I b) Find the indefinite integral (2x+3)dr...

A: To evaluate the following integral.a ∫012x4-2 dxb ∫2x+3 dxc ∫0x et dt 

Q: Below is the function f(x). -6 -5 -4 -3 -2 -6- Over which interval of æ values is f' > 0? O (1, 0) O...

A: The graph of the function is 

Q: Let F = (3x, 3y, 6z). Calculate div(F) and curl(F). (Use symbolic notation and fractions where neede...

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Q: The alternating series (-1)" . converges. (You do not need to prove this, but you can if you 1 3" n ...

A: Here, the given series is: ∑n=1∞(-1)n13nn Now, the given series is an alternating series with 13nnn=...

Q: Use traces to graph and name the surface

A: The given surface is: x24-y29+z216=1...(1)

Q: Use the properties of natural logarithms to simplify the function. f(x) = ln(x/4)+ln(4)

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Q: 00 Determine whether the series E. 2 converges or diverges. If it converges, find its sum. e n= 0

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Q: Is the function f (x) below continuous on [3, +∞)? (0, x > 0 x, 0 3 Choose Choose Choices Yes nuc No...

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Q: The estimated revenues r (in millions of dollars) from sales of in-vehicle technologies in a certain...

A: Given that, The revenue function is following, r = 157.49t2 − 395.5t + 6129,            3 ≤ t ≤ 8 We...

Q: D. Evaluate et-2 tan vE 2t + 3 S 't² – 2t + 1 e2t

A: To evaluate: ∫et-2e2t, tan tt, 2t+3t2-2t+1dt=∫et-2e2tdt, ∫tan tt dt, ∫ 2t+3t2-2t+1 dt+A,B,C

Q: Select ALL possible answers. Which of the following is lare NOT true of the function f (x) whose gra...

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Q: lirectly using the calculator, compute the zero- through fourth-order approximation of v7. For each ...

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