Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

Q: Assuming that a DE has a general solution a+y= 3r +C, what is the particular solution at given the…

A: Explained below

Q: A hole of radius 1 inch is drilled through the center of a spherical wooden ball of radius 3 nches.…

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Q: Sketch the region enclosed by Y 6x and y = 9x". Find the area of the region.

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 9y and…

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Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: Given that the number of bacteria in a certain population increases according to a continuous…

Q: Mark the critical points on the following graph. | 20- 16- 12- -5 -4 -3 -2 -1 2 3 -4 --8- -12- 16

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Q: The curved portion of the v-t curve shown in the figure are second degree parabolas with horizontal…

A: answer is in next step

Q: x² + y³. 2 = Consider the surface S of equation (1, 1, v), An equation for the tangent line tangent…

A: We have to find the equation of tangent line.

Q: Solve for the gradient of the given function. f(x, y) = e¤ sin y + el cos x

A: Given,  f(x,y)=ex sin y+ey cos x

Q: derivatives as functions of

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Q: -2000x has the marginal-demand function D'x)= where Dx) is the number of units sold at x dollars per…

A: First we'll integrate and the we'll put the given value. So i am providing my handwritten notes…

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: A company that produces cell phones has a cost function of C = 6x² – 197x + 1859, where C is the…

A: C= 6x2-197x+1859differentiating w.r.t xC'=12x-197+0C'=012x-197=0x=19712

Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point.

Q: Solve the system of equations using matrices (row operations). 3z- 3w = - 4 X+ y+ z+ 3w= -1 2x + y-…

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Q: Let 7 (t) = Find a parametric equation of the line tangent to 7(t) at the point (– 27, – 44, 1.792)…

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Q: 3 (2). Consider the solid Q bounded by the surface of the equation y =x² + z? and the planes, zV3 =…

A: Here's the solution... please have a look at it.. Answer: option C

Q: d d ri(t) - r2(t)] and nt) x ra(t) first by differem [ri(t) × r2(t)] first by differen dt dt the…

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Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

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Q: The slope of the tangent line is

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Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x². Make a sketch and shade in…

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Q: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

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Q: Show that lim (2,v)>(0,0) **+y D0.

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Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: (235 – 4.x25 + 2x)dx

A: The detailed solution is given below Thank you

Q: It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the…

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Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

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Q: 1. A bumblebce was released and started to travel along a straight horizontal line. The directed…

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Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A: Topic:- application of derivatives

Q: 11. Use the guideline in §4.4 to sketch the curve: f(x) = x² ln x. A). Domain, Symmetry, Asymptotes,…

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Q: Determine the equation of the midline of the following graph. 2 -27 3 27 3' 47 3 3. '3 2 6. -1 -3 -4…

A: From the given graph we have to find the midline value

Q: What is the area of the region bounded by the graph of r = 4 cos 20? Choose two (2) correct answers.…

A: Let's find.

Q: Consider the following equations. y = -x2 + 2x + 1 y = -x + 1

A: Solution: y = -x2 +2x +1 y =-x+1

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: F. dr. Evaluate Jc F(x, y) = xi + yj C: r(t) = (3t + 8)i + tj, 0 sts1

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Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

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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. %3D - V · (F × G) = %3D

A: To solve the following problem

Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: sider the function f(x) 3x on the interval |- 2, 2]. Find the average or mean slope of the ction on…

A: Topic:-  derivatives

Q: Find the area of the shaded region 10x) = 8x - 2x - x, g0x) = 0

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Q: dy If dæ 4x³ + 3x? + 6x and y = -3 when x 1, fınd y. |3D

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x, x = 1, and y = 0,…

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Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

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Q: (i) Using Laplace's equation, find v,and və for inviscid vortex flow.

A: answer is in next step

Q: Write the augmented matrix for the system of linear equations. 6x +y+ 3z =D 2 9x - 6y- z = 5 x-8y-6z…

A: Explained below

Q: The ellipse shown below has parametric equations x(t) = A cos t, y(t) = B sin t, 0 <t< 27.

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Q: The surface S is parametrized by equations x = u + v, y = 3u?, z = u – v; The point P (2, 3, 0) lies…

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