Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = Vx y = 0 x = 3 (a) the x-axis (b) the y-axis (c) the line x = 3 (d) the line x = 9

Q: Consider the solid a drawn in the first octant, as shown below, which is formed by the surfaces y =…

A: We have to find the mass of the solid.

Q: y6 16 (1). Consider z as a function of the variables x, y which is defined by z = ln(x®y) + and let…

A:

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: 8. If V represents the volume of an object, what does AP represent? - dt

A: dydx-Represent the Rate of change of 'y' with respect to 'x'. Here, 'y' is dependent variable and…

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: dy 3. Use logarithmic differentiation to find dx for y= Vxe* (x' +1)"

A:

Q: 3 For the given equation f(x) = x³ +a2 %3D 6x + 10

A: f(x)=x^3+3/2x^2-6x+10 f'(x)=d(x^3+3/2x^2-6x+10)dx f'(x)=3x^2+3/2(2x)-6(1)+0 f'(x)=3x^2+3x-6 take…

Q: Let ü = - 4 and i 3 , and let w = ü x v. Answer the following: Find w. Give your answer as a vector…

A:

Q: cOs x dx sin² x+ 2 sin x+5

A:

Q: ind for by Implicit differchtioution 2(xu)

A:

Q: Double USA, manufacture of the Nicolas cage pillow has determined that the marginal daily revenue…

A:

Q: The circumference of a sphere was measured to be 81 cm with a possible error of 0.5 cm. Use linear…

A:

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: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

Q: A particle's position at time tis given by r(t)= (3t",4t+1,-t). Find a, att=3.

A:

Q: x2 + x – 2 At which value of x does the function f(x) have a removable discontinuity? g3 – 3x2 + 2x

A:

Q: —2х Se-2x sin 3x dx

A:

Q: Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č =…

A: Given query is to find the volume of the parallelopiped.

Q: undamental set of solutions of a homogeneous linear nth-order differential equati mprises(Choose…

A:

Q: Find the area of the specified region. sec e Inside the dircle r 3 and to the right of the line r =…

A:

Q: Find the area of the region enclosed between the curves defined by the equations y = vx +2,y= x ,…

A:

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: Consider the change of variable u = xy and v = 3y + 2x and the integral 2.r + 3y – 6 =0 - ||. (2r²y…

A:

Q: If y = xe'* is a solution of a linear homogeneous 2nd order DE, then another solution might be A. y…

A: For a second order linear homogenous equations, If roots of auxiliary equation are 1. real and…

Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Consider the double integral XY dA Vx2 + y² I where R is the region of the XY plane, given in the…

A:

Q: In t years, the population of a certain city grows from 700,000 to a size P given by P(t)= 700,000 +…

A:

Q: 4. The path of a baseball relative to the ground can be modelled by the function dlt) = – f² + 8t +…

A: derivative

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: Oil is leaking out of a ruptured tanker at the rate of r(t)=40e^(-0.03t) thousand liters per minute.…

A:

Q: Determine whether the vector field F(x, y, z) = (y + z)i – xz°j+ (x²siny)k is free of sources and…

A:

Q: A lighted candie burns outr according to the equation y'(1) =ky (1) where y is the length (in…

A: see below the answer and explanation

Q: dy y- 2x. dx = x(x+1)y %3D

A:

Q: Find the value of the specified finite sum. Given ak = 3 and bk = 7, find (ak- 2bk). %3D k=1 k=1 k=1

A: We can find the specified finite sum as below.

Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

A:

Q: Find ke ende finite integral. cuse c for Ge Constant of entyration) J Sin 39 Jcos 34 de (the + are…

A: We need to solve integral.

Q: /1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0<t <1.

A: Use the parameterization of curve for finding the length of curve .

Q: 55. At 9 A.M., ship B is 65 miles due east of another ship A. Ship B is then sailing due west at 10…

A:

Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -

A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: encourage new members a bank offers a savings account of 2.4% interest mpounded monthly provided new…

A: We will determine the account value after 10 years.

Q: Find the derivative of f(x) = (2 - 3x) (-5x + 4). O 2 О 22-30х О зох + 22 30x + O 15x + 8 None of…

A:

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A:

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We have to find the limit

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[8t^2 e^-2t]

A: Laplace transform of the function f(x)Lf(t)=∫0∞e-stf(t)dt

Q: Find f such that f'(x) = f(4) = 20.

A:

Q: y = C,x + C2xlnx is a two-parameter family of solutions of a DE on (0, 0). What would the values of…

A:

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

A: