Use a double integral to find the volume of the indicated solid. 9. z = 9-2 y 2. y=2 4 X=4

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

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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: Given

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A: Gradient

Q: (b) A spring exerts a force of 4.2N when stretched 0.7m beyond its natural length. How far beyond…

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Q: Find the limit. lim (ti – 3j + r² k) 1-2 lim (t i – 3j+r k) = i+ j+ i k %3D i

A: The question can be solved using the concept of limits.

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). 3 r(t) = e%i+ ej %3D K(t)

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Q: r=1+ 3sino

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Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: In this question, the power series method is to be applied to find the general solution of a…

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Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

A: Use the washer method to find the volume of rotation of the solid.

Q: 8 cossa da V sin a

A: Integral

Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: The Taylor series for cos(x) centered at a = 0 is given by: (-1)",2n (2n)! n=0 Using this result,…

A: Given problem:-

Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

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.

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: Use double integration to find the volume of the solid. ... 3x + 2y + 4z = 12

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

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

A:

Q: d. Calculate ri(t) · r»(t)] and d Edit dt [r1(t) x r2(t)] first by differentiating dt the product…

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Q: Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

A: We need to evaluate integral.

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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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: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

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: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: bounded by the graphs of the equat y

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

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

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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: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

A:

Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given

Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: Evaluate the iterated integral. 4ze dy dx dz

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Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x' and…

A: Solution:

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

A:

Q: Find the area of the region enclosed by x² and y integrating with respect to y. the curves Y = 4x by…

A: A detailed solution is given below

Q: True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel…

A: We have to state whether the given statements are true or false: Statements are as follows: 9. A…