Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate planes and the plane 21x + 42y + 10z = 420. NOTE: Enter the exact answer. V =

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.

Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Consider the limits. lim f(x) = 6 x-7 lim g(x) = -8 x→7 Evaluate the limit using the limit law for a…

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Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

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: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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

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Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

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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: Determine the derivative of у. /20x+6 y = ev y =

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

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Q: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

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Q: find the equation for x in y=3x-x^3

A: Solving

Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: dx 2.

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Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

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Q: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Find V· (V × F), if F(x, y, z) = 7e2*i+9xe³j – e=k. V · (V × F)

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

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

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Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

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Q: Find the area of the region inside the circle r = 12sinθ and outside the cardioid r = 4 + 4 sinθ.

A: Area

Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: Given:          Curve y=2x2+10                     y=4x+16

Q: 7. -4 3. ) -3 7. 1) 10. 2)

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: If f is continuous at a number, x, then f is differentiable at x. True False

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different way dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: xe*y dy dx

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Q: Sketch the region enclosed by the curves and find its area. y = cos 4.x, y = 0, x 8' 4 NOTE: Enter…

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