Find the volume of the solid generated by revolving about the y- axis the region bounded by the graph of y = 3x - x3, the y-axis, and the line y = 2.

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Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

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Q: i(x) = 2-0.8(x-43.79)

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

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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: 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: 1+9n² b) Determine whether the sequence a, = converges or diverges. If it converges, %3D 1+n find…

A: The given sequence is: an=1+9n21+n2

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

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Q: H.W (5) Solve the following differential equations of ay (6x-y+3)dx+(3y' -x-2)dy 6) Integration…

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Q: For each sign chart for f. Carefully sketch the graph of both functions f and f. Upload your work as…

A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

Q: 2. Use the Divergence Theorem to compute ffs F. dS for F = (xy, yz, x² z + z² ) and S the boundary…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: 3x?+4x-7 ii) lim x2+9 X00

A: Given query is to find the value of the limit.

Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

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Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

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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: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

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Q: Describe the graph of the equation. r = 7 cos t i – 17 sin t j +k O An ellipse in the plane z = 1,…

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Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

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Q: d d Calculate r1(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find k(t). 13 r(t) = e"i+etj K(t)

A: Solving

Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

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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: x+x-6 lim X-2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

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Q: Find the derivative of this function

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: dy If y = 3e5 . Find dz

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

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

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Q: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

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Q: Find div F and curl F if F(x, y, z) = 3e"Y i – 6 cos yj+ 10 sin? z k. div F= curl F=

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Q: d²s = 60/E – 18 subject to the conditions that ds = 5 and s= 11 when t= 1. Find the velocity v = dt…

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Q: The velocity of a car is v(t) = 42(t - 2)(t - 4) miles per hour on the time interval [0, 4] hours.…

A: We need to find distance traveled by car.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y³, P(4,…

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Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

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Q: lim 48V x 487Y

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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