Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by f(x) = 6 sin (Tx), the r-axis, the y-axis, and the line z = 1 around the y-axis.

Q: Find the angle between u and v in radians. u = 4j - 2 k, v = 8 i - 3 j- 10 k O 0.14 1.43 1.57 1.53

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Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 4 %3D k! k=0 4...

A: Taylor's series about x=x0 for the function ex; x0=4

Q: Find the function f(x) such that  f ′(x) = f(x)(1 − f(x)) and f(0) = 1/5.

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Q: Find the sum of the convergent series. 9+0.9 + 0.09 +0.009 +.. .

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Q: Use sigma notation to write the Taylor series about x xo for the function. e; xo = 7 - 7)* k! e7 k! ...

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Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)...

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Q: Convert each degree measure into radians. 13) -780° 14) 345° 15) 150° 16) -250°

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask th...

Q: Use sigma notation to write the Maclaurin series for the function. 9coshx 9. –1) (2k)!" 6. k=0 00 2k...

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Q: Find the absolute maxima and minima of the function on D, where D is the closed triangular region wi...

A: Maxima minima

Q: Let R be the region inside the polar curve r = 4 and outside the polar curve r = 4+2 cos 0 as shown ...

A: Consider the figure given below : We need to calculate the shaded area from the above figure.

Q: esec-1 d.x. xVx2 – 1 1

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Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af...

A: Topic:- partial derivatives

Q: 2ea dx (ет — 1)2 1

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Q: If Ax) = x² + 3x – 2 and g(x) = X+2 then g(f(-1)) is equal to 6.

A: The objective of the question is evaluate the value at the given functions of composition.

Q: whether the geom 08. (-7)" – 1 Σ 8" n = 1

A: Solution is given below:

Q: Н. Š(-1)"10" п! n=1

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Q: f (x) = 2x? – x +6

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Q: 1 -dx Use the technique of completing the square to evaluate the following integral: J x2 - 6.x

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Q: 5x Determine the values of x for which the function f (x) = is discontinuous. x2+x

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Q: Q4 Let f : R → R be the function defined by 1 f(x) = a) Is f is one-to-one? If yes, then explain why...

A: topic - onto functions

Q: the series using any appropriate test from this chapter. Identify t t with the p-series

A: We have to choose the correct  options according to the given information

Q: Sg(x) dx 2. g(x) 3. 3f(x) dx 5. If(x)-g(x)] dx 6. [4f(x)– g(x)] dx

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Q: Find all the first order partial derivatives for the following function. f(x, y) %3D хуе "У af dy af...

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Q: C. Find i '(t). 1. ř (t) =

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Q: QI) Find the volume of the solid generated by revolving region bounded by the curve (x-Jy)& the line...

A: Volume

Q: For the function y =f(x), it was found out that f(c) = 0 and f'(c)=5. What can be said that x-c ? cr...

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Q: 2. If cos 4A = 23/49, find tan A %3D

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Q: Find the indicated vector. (-1, 6), v = (1, -8). Find - u - 9v. O (-8, 66) O (5, 63) O (10, -78) O (...

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Q: ii. find the equation of the tangent line to f at x = a. (a) f(x)=3-4x, a=2. (b) ƒ(x)=x² +x, a = 2.

A: We have to determine the equation of tangent line 

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u ...

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Q: Find the derivative of the vector function below r(x) = sin (secx ²)i +csc°(Vx² +1)j +8tan(x' k

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Q: tanwdw The is equal to 1- tan?w

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Q: Determine the amplitude, period and displacement for the given function, and sketch the graph of the...

A: Function y=32sin2x+π6 is given.We have to determine amplitude, period and displacement for the given...

Q: Find an equation for the sphere with the given center and radius. Center (0, -3, -6), radius = 9 HIN...

A: The equation of a sphere is  (x - h)2 +(y - k)2 + (z - k)2  = r2 Where (h , k , l) is the center of ...

Q: C. Find i '(t). 1. ř (t) =

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Q: 4. If cos 4A - -1/9, find cos A 5. If tan 4A - 24/7, find sec A

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Q: To integrate v3 x2dy we apply integration by parts and in the form u dv, u is set as: 2 of 11

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Q: Determine the present value P that must be invested to have the future value A at simple interest ra...

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Q: 1 -1 -2 -2 -1 0 1 2 3 2 3 4 4 -2 -1 4. FIGURE 6.1.12. Spiral point (-2, 1) and saddle point (2,-1). ...

A:   Given the systemdxdt=2x-2y-4 anddydt=x+4y+3 To find critical point we take dxdt=0 anddydt=0  

Q: Use the 2016 marginal tax rates to compute the tax owed by the following couple. A married couple fi...

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Q: Given the function y=f(x), y' is found to be negative over the interval (4,8), then over this interv...

A: we have of cheek and find answer

Q: Given f (x) = sin x and g (x) = cos x, show that f (g (5)) = 0. Show all your %3| steps.

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Q: Find the indicated vector. Let u = (8, 3), v = (8, -6). Find v - u. (-5, -14) (16, -3) O (-14 5) O (...

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Q: Find the area inside the curve r = a(1+sin theta) and outside the curve (r =a sin theta). 6:01 PM

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Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*...

A: We can answer all three subparts as below.

Q: tanwdw The is equal to 1 – tan?w A. In (Vsec2w) + C B. In (Vsec2w) +C C. In (Vsec2w) + C D. In (Vtan...

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Q: Solve the problem. Find the area of the triangle determined by the points P(-3, 6, -4), Q( 2, 10, -9...

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Q: Question 2 tan (0) Insec(0) do A -Incos (0) + C 2 B - (Insin(@)) ² + C - (Intan( @)) ² + C D (Insec(...

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Q: Write a chain rule formula for the following derivative. du for u = f(x); x = g(p, q, r) ar du du ar...

A: We have to choose correct option