3.18 Find the gradient of the following scalar fields and evaluate the gradient at the specified point. (a) V(x, y, z) = 10xyz – 2x²z at P(-1, 4, 3)

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About th...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A: Telescoping series is the series in which all but the first and last terms cancel out .

Q: A company makes computer chips from square wafers of silicon. A process engineer wants to keep the s...

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Q: 10. Se** x? dx A C. 2 e* + C ex + C 3 e** + C e** + C O A Ов Ос OD OE None 112 1/3

A: We can evaluate the given integral by using the substitution u = x3 and the following formula.  

Q: du What is the value of u, given the equation equal to? A. x² В. 4 С. 6 D. none of the above

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12 – x...

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Q: À searchlight is trained on the side of a tall building. As the light rotates, the spot it illuminat...

A: Given problem:- A searchlight is trained on the side of a tall building. As the light rotates, the s...

Q: Find a value of x, if any, at which f (x) = Vx – 125 is not continuous. If f(x) is continuous for al...

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Q: 1. Use any appropriate method in finding the indicated solution of the following differential equati...

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple quest...

Q: Find the first partial derivatives of the function. f(x, t) = Vx In(t) 1 cln(t) 2Vx fx(X, t) fe(x, t...

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Q: Let U be the universal set such that any set is a subset of U. Let A and B be sets. Usc element argu...

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Q: 15 tind the voleime of the solid senerated by revoling the following region about the y-axis, The re...

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Q: Find the area that are bounded by:  y=x2+5x and y=0 from x=−2 to x=1.

A: Given: - The curves are,y=x2+5x and y=0 from x=-2 to x=1 To find: - The area that area bounded by gi...

Q: Evaluate the Integral dx 7. S xVx+6x ANSWER: 1 7. ÷ In 3 + C x+6

A: Given: I=∫dxxx+6x   ...1   We know that; ∫1ax+bdx=1alnax+b+C

Q: 8. Evaluate the integral 2y dA where R is the region between the curves y = x2 and y = x(1 – x).

A: As per company guidelines we can solve first question. I hope that the given solution will help you....

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (- 1)k+1 k9/8 ...

A: The given series is  ∑k=1∞ (-1)k+1k9/8

Q: 8) A company's demand equation is x - V 2000 - p² , where p is the price in dollars. Find dp/dx when...

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Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: 1800 + 500, where q represents the demand for the product, find the marginal revenue when the demand...

A: To find out the marginal revenue. 

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: We need to find Tylor series.

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 4 Pa(x) =

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Q: Evaluate: (2x + 1)3 dx by two methods: 11) let u = 2x + 1 %3D 12) Expand (2x + 1)³ Compare the resul...

A: Integration

Q: Given f(x) = 2 /x + 2, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A:  Given: x=13yy-3

Q: In each part, evaluate the expression given thatf(5) = 9, g(5) = -1,f' (5) = 18, and g' (5) = -9. %3...

A: Since you have posted multipart questions i can do first three subparts as per our company guideline...

Q: Find the average square distance from the origin to a point in the domain D in the figure. Assume a ...

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Q: find solution of this differential equation:  y′ tanx sin2y = sin^2 x + cos^2 y

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Q: imination of arbitrary constants = cjxe2* + cze¯*

A: Please refer to the image below

Q: Lm e7x dx 00

A: This question is based on definite integral.

Q: 13) The marginal cost function for a particular commodity is given by C'(x) = 6x-17. If the cost of ...

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Q: et dx Ve²x+49

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Q: 8x3 dx The J using the substitution u = 5 – x* is ..

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Q: Question 12 Provide an appropriate response. Is 5x4 dx =x5? Explain your answer. Use the editor to f...

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Q: (6 points) Delermine whether the series is convergent or divergent. If it is econvergent, fin um.

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Q: 5. 3x2+x-1 SC x+2 3x2 3x2 + 5x + 9 In Ix+ 21+ C 2. -5x +9 In Ix+ 21+C 2. 3x2 D 3x2 9. 6. + 5x + +C 5...

A: Given: I=∫3x2+x-1x+2 We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫ax+bndx=ax+bn...

Q: The total amount of money in circulation for the years 1990-2012 can be closely approximated by M(t)...

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Q: 1 dx Ji x/1- (In x)²

A: ln x = tdxx = dtx=1 → t = ln 1, t=0x=e → t = ln e, t=1   I = ∫01   11-t2  dtFormula:∫ 1a2-x2  dx =1a...

Q: Question 8 Which of the following is NOT EQUAL to the given integral. tanx There is no correct answe...

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Q: c. Evaluate the integral. 4 c3 4. S S(x² + 3xy²)dxdy

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Q: y''-4y'+20y=x^2e^(-2x)sin(4x)-3cos(4x)-xe^(-2x)

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Q: 2x – x3 1. Evaluate dx. (r – 1)²(x²+1). -

A: we want to find the value of the given integral I=∫2x-x3(x-1)2(x2+1) dx

Q: 4. S (sint + cost t ) dt A - cos t + sin t + C C - cos t- sin t + C B cos t+ sin t + C D cos t- sin ...

A: 4. In this question, we need to find the integral.

Q: Suppose that a population of bacteria triples every hour and starts with 200 bacteria. Find an expre...

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Q: (x- 2)" (n+ 1)3" n=1

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Q: PLEASE USE  INTEGRATING FACTOR FOUND BY INSPECTION , NOT LINEAR , NOT HOMOGENOUS NOT ANYTHING. JUST ...

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Q: ydx + 2(y4-x)dy=0

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Q: Vx + 9 dx dy The answer should be in the form ' S S(x, y) dy dx, where a < x < band 81(x) < y < 82(x...

A: We will evaluate the double integral. 

Q: A graphing calculator is recommended. A particle moves according to a law of motion s = f(t), t 2 0,...

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Q: 1 6. S -dx (x+1)(x²+1)' 2x+1 7. S dx (x+1)(x²+2)

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