Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations. z = x + y x2 + y2 = 64 %3D first octant V = dy dx =

Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: around the boundary of the parallelogram in the following figure (note the orientation (X9.Y), (2.0,…

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Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: Find the area inside the circle r = = cos 0, but outside the circle r = 1/2. Sketch the graphs first

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Q: Use the first six non-zero terms of the Maclaurin series expansions for sin x and cos x to…

A: From the Maclaurin series expansion of sin x and cos x: sin x≈x-x33!+x55!-x77!+x99!-x1111!cos…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3 y…

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

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Q: Use Ore's theorem to prove that any n-vertex graph G for which |E(G)|> (",') +2 is Hamiltonian.

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Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

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Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: Find curl (8z i + 9xj+4y k). curl(8z i + 9x j + 4y k) = ( i )i + ( i j+( i )k

A: topic- curl of a vector

Q: Find the absolute maximum and absolute minimum values of f on the given interval. ex f(x) [0, 6] 1 +…

A: maxima minima

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ei + Sin(/2)j + e stk…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

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Q: The graphs of the function f (r) = 7- a and g(a) = 3 are given below. %3D 10 8 f(x) = 7-x2 4- g(x) =…

A: topic- area bounded by curves

Q: lim (3x + 1) sin(2x) 4x2

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Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

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Q: Determine the value(s) of x where the tangent to g(x) = (x + 5)(x2 - 1) is parallel to y = -7x - 8

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (5t + 6)i + tj, 0sts1

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Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

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Q: Evaluate the integral: (5si + 9s²j + 10k) ds Answer : i+ j+ k

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

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Q: (b) trte) × u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

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Q: dy If y = 3e5 . Find dz

A: Given query is to find the derivative of the expression.

Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

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Q: sec'xdx

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Given :r(t)=6costi+6sintj

Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p…

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Q: Find r'(t) %3D r'(t) = %3D

A: Given;  r(t)=6 sqrt(t)i +t2 sqrt(t)j +ln(t2)k.

Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

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Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

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Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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Q: Explain why the Comparison test is not a good choice for showing that the following series…

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Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

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Q: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: solution

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Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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