2. The integral S,n(4 - y²)?dy represents the volume of a solid. Sketch the region, rectangular element, and axis of revolution that produced the solid. Label your graph.

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will…

A: We have to find the dimensions of the cylinder.

Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

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Q: 5. Find the solution of the following initial value problems. F'(u) = 4cosu – 3, F(0) = 4

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Q: 1. a. Show that two lines with direction vectors d, = (2,3) and d, = (6,-4) are perpendicular. %3!…

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Q: 12 dx Jx3 – 3x2

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Q: Let W = (a + bxr +x? € P: a,b ER) with the standard operations in P2. %3D Which of the following…

A: W is not a subspace of P2 because 0 does not belong in W.

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: 3. Let C be the line segment starting at (0,0) and ending at (1.3) (see diagram). Find a…

A: The line passing through (0,0) and (1,3) is given by: y=3x which in parametric form is given by:…

Q: Use any method to solve the following system of equations. 2x2 +y? = 5 x2 - 2y? + 15 =0 Select the…

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Q: Find the solution set of the following linear system. Identify inconsistent systems and dependent…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about…

A: Given:-the region bounded by y=sinx, x=0 and y=1revolving about y=1using washer/disk…

Q: Find the linearization L(x,y) of the function f(x,y) = e 4x cos (7y) at the points (0,0) and 0,- ...…

A: To find the linearization Lx, y of the function fx, y=e4x cos7y at the the points0, 0 and 0, π2.

Q: Find the Taylor series generated by f at x = a. 1 a = 4 f(x)= x

A: We are asked to find taylors series of the function

Q: Find the net signed area between the graph of the function f(x) = |x +3| – 4 and the r-axis over the…

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Q: Evaluate the following integrals i. L Ix| e(1+x*) dx -0.5 ii. So x cosh(x² + 1) dx

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Q: Triangle BAC is a 30°°-60°°-90°° right triangle. В 600 300 A C If BC = 15, what is the measure of…

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Q: Ryan is puréeing different fruits and freezing the purées in ice cube trays. He knows that the…

A: Volume of each frozen cube = 1.5 cubic inches. We have to find the volume of the kiwi fruit and then…

Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) =x, a = 3 %D O A. P3(x) = 1 + 6(x-…

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Q: Find the derivative of the function at Pn in the direction of A. f(x.y.z) = xy + yz + zx, Po(2, - 2,…

A: The  derivative of f at the given point is given below.

Q: The function x2 f(x) = 1 - x has a local maximum when x = 2. Select one:

A: We will check if the given statement is correct.

Q: Given the differential equation dy dx (x – 1)(x + 2)' x +1 y = 1- y > 1, x> -1. a) Find the solution…

A: Here we have given a linearly differential equation :

Q: the

A: We will find the distance.

Q: Assuming that out of 200 documents, 40 documents are relevant. A search engine returns 30 documents,…

A: Number of relevant items retrieved =12Total number of relevant items = 40

Q: Sf(x)dx = 2, f(x)dx = -5, and ſ g(x)dx = 1 . Evaluate the following 7. Suppose integrals. SF(x) +…

A: Here we have to find the given integral. I have appended the formula used in the solution part of…

Q: The function x2 f(x) 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: Sketch the region enclosed by ?=5?y=5x and ?=3?2y=3x2. Decide whether to integrate with respect to…

A: Given: y=5x, y=3x^2

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. You must show your work.…

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Q: The interval of convergence of the series 41+2n (x+3)" is - -- 5n+1 16 16 Select one: O True O False

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Q: lim X- Sin X X3

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Q: 72 a, = 5, an +1-1+ an

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Q: Find the linearization L(x,y) of the function f(x,y) = e 4* cos (y) at the points (0,0) and 0, The…

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Q: Current Attempt in Progress 9. Find f(2x + 4)dx if f(x)dx = 3. Enter the exact answer. f(2x + 4)dx…

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Q: I d (Cot x) (COS X dx sin X * Sin x (-sin x)-cos x (cos x) (Sinx) (sin*x + ças* x) Sinx + Cos x )…

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Q: af Find if f(x,y) = ysin xy

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Q: 2x-9x+2= 4x-13

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

Q: Question If you were to use a substitution of u = cos(x) to evaluate the definite integral below,…

A: Use the given substitution to find the new limits

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ –…

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Q: need the answer quickly

A: Solve the following

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: topic- application of derivatives

Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: Find all the second order partial derivatives of the given function. f(xy) =xy° +y¢* +5 O A. f = 2x,…

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Q: Given: (6, 0, –2) and (0, 8, 0). (6,0, –2) × (0, 8, 0) = æi + yj+ zk. Find x +y+ z.

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

A: To find out the correct options.

Q: n3 + n? ) Σ 00 (n – 1)! n=1 2n + 3 n2 In n n=1

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Q: 20 22. cot 3 - V3 -

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Q: aw aw aw I. Find дх and and (whenever possible) for the following functions. ду dz 1) w = 5x*y –…

A: Since, you have posted multiple questions. As per guidelines we"ll solve only first part. If you…

Q: ind the values of a and b so that the function = x + ax + b has a local maximum at the (-16,- 12).

A: We will find the value of a and b.