Consider the cOnservative vector field F(r, y, z) = (2xr, z, y). %3D a) Determine a potential f such that Vf = F. b) Compute the line integral foF - dr over the curve C parametrized by F't) = (t°, e', e"), 0

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Q: 2- 6

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A: Put x=r cosθ  and y=r sin(θ). As x,y→0,0 then r→0+. L'Hospital Rule :Suppose we have          limx→...

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A: To evaluate ∫36dxx4+3 using Simpson's Rule for the value N=6 Simpson's rule formula is: ∫abf(x) dx≈S...

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Q: A type of sugar in the blood, also known as glucose, which is one of the major sources of energy, is...

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Q: If f(t) = (t + 7t + 3) (5t? + 4), find f'(t). %3D Find f'(1).

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Q: (g) Graph the position, velocity, and acceleration functions for the first 8 s. y y 40 40 a 20 20 4 ...

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + • 6 1 1 + 8 · 10 + + 2. 6 · 8 (Use symbolic notatio...

A: The given series,    12.4+14.6+16.8+18.10+......

Q: d/dx[(sin x)/(1 - 2cos x)] = (cos x - 2)/(1 - 2cos x)² Select one: O True O False d/dx(xe2x) = 2xe2x...

A: We know that; The Power law: ddxxn=nxn-1 The chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f...

Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula...

Q: Sketch the graph of each of the following functions. (a) f(x,y) = cos x (b) f(x, y) = 3x? + 3y? – 6x...

A: Sketch the graph of function

Q: d/dx(3x) = 3 Select one: O True O False d/dx[(x2 + 5x)/(x - 8)] = (x² - 16x + 40)/(x² - 16x +64) Sel...

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Q: Section 2.9 p. 252/254 # 398 For the following exercises, find the antiderivatives for the given fun...

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Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans ...

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Q: &r4- V Let y=f (x) + C be the antiderivative of F (x) = determine the value of C (use 3 decimal plac...

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Q: 7,055 is a large number. O Command O Opinion O Suggestion O None of the choices O Statement O Questi...

A: It is an opinion.

Q: 19. Use the method of Lagrange multipliers to find the extreme values of f(x, y, z) = 4x + 2y + z, s...

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Q: 12. Sketch a picture of a graph y = f(x) that satisfies f'(-1) > 0, f'(0) = 0 and f'(1) < 0.

A: Follow the procedure given below  

Q: Find the tangent line to the curve y = 2x - x? at (2,0)

A: We can find the required answer as below

Q: хуdx — (2x? + у?)dy — 0

A: Follow the procedure given below.

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the...

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: Verify each differentiation formula d -u (a) [Arccos(u)] = dx V1-u? (b)(Arccot(u)] = d -u dx 1+u² -u...

A: As per the instruction, we will be answering the first one. For (1), For (a), arccosu' =-11-u2×u'   ...

Q: d²y 4 + y = t2 –- 2t + 3 dy - dt2 dt

A: As per the guidelines, are supposed to solve only one problem, please re-post the other problems ind...

Q: Verify the following general solution, then solve. Find the particular solution to the differential ...

A: Let's find. 

Q: y 6- 5 4. 3+ 2 1 1 3 4 5 6. 7 Graph of g The figure above shows the graph of the differentiable func...

A: Graph of G is given.We need to find the value of a by using the given conditions.Below find the deta...

Q: To test this series for convergence n4 + 3 n=1 1 where p= You could use the Limit Comparison Test, c...

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Q: Calculate the integral using a hyperbolic substitution. (Express numbers in exact form. Use symbolic...

A: To evaluate the integral.

Q: The cost, in dollars, of producing x units of a certain item is given by C (x) = 15x - 4VE – 9. Find...

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Q: D. Tell if the function is continuous at given interval. 31-35 2x+4 [-2,2]

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Q: Show a complete solution for each item. Determine whether each of the following functions is (a) con...

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Q: Completely simplify the expression: cot(x)+tan(x) sec(r) Ocsc(x) 2 sec(x) O csc(x) O sec(x)

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Q: In(x) f f(x) = x10 ='(1) = 2, find f '(1). %3D

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Q: 3. lim f(x) = -2, lim f(x) = 2 and f(2) = 0 4. lim f(x) = +∞, lim f(x) = -00 X-3- *- 2+ Y 3+

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Q: Limit that nate ASSESS WHAT HAVE YOU LEARNED to Bvaluate the following limits by constructing their ...

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Q: Find the soIltion to the following equations: %3D iv)6=多はら

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Q: The solution to the differential equation dy t - 1 dt 2y is IS

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Q: Solve the given differential equation. x?y" + xy' + 36y = 0 y(x) : ,x > 0

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Q: Name and graph the following quadratic surface. 9x2 + 4z2 – 36y = 0

A: For (b) Sketch of z=9-x2-y2: The graph is a paraboloid.

Q: Find the quotient and remainder +3x-215 divided by ナセーッメ When x+3. you may use 2en how elther Poiyno...

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Q: Find a bound for the error in the approximation M10 to the given integral (but do not calculate M10)...

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Q: V1-x? 1 x2 + 1 1 X.

A: Follow the procedure given below.

Q: Find the MacLaurin series of f(x) = sinh(3x) . Express your answer in the form Σan (x - c)^n. The pr...

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Q: find the equation of the tangent line and normal line to the ff. curves at the indicated point.

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Q: Consider the equation below. 16x2 + y? + 16z2 - 8y – 160z + 400 = 0 Reduce the equation to one of th...

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Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line. ...

A: topic - derivative of a function and point of horizontal tangent line