z = 16 - x2 - y2 10 -8 1768 46 8

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: FOTE: Enter the exact answer. dx dy = VT

A: A detailed solution is given below.

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

A: Given: y=2x-6x=0 and x=4

Q: Find the directional derivative of the function at P in the direction of v f(x, y) = x³ - y³, P(6,…

A: we have to find directional derivative.

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: A tank originally contains 100 gal of fresh water. Then water containing - Ib of salt per gallon is…

A: Given , A tank originally contains 100 gal of fresh water. Then water containing (1/2) lb of salt…

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

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Q: 5² - 13 ニ

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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: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

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Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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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: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: Finden- un) andrn - in twe dferent mays r(t) -n+ se's - e'N, wt) - t'k (a) re) - uch) () Find the…

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Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

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Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

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Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

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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: |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

A: Given problem:-

Q: lim 48V x 487Y

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Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

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Q: Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

A: Given curve r= 1+ 3sin( theta)

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

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Q: Use the gradient to find the directional derivetive of the function at Pin the drecton of v n(x, y)…

A: Directional derivative of a function f(x,y) at a point P(a,b) in the direction of the vector v=ai+bj…

Q: Jse a double integral to find the volume under the plane z = 38x + yand over the rectangle R = {(x,…

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Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: The position vector r describes the path cof an object moving in space. Position Vector Time r(t) -…

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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: 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: Find fr(t) u(t)] and fr(t) x u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A: Vector

Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

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Q: Question 4 Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: This question can be solved using the concept of volume of solid of revolution.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: r=1+ 3sino

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. 30…

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Q: 1-sine Evaluate the iterated integrals J. J. r2 cose dr de A) 1 B 2 c) o D) 3

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Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) =…

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