Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve x = 5y-5y³ and the y-axis about the given axes. a. The x-axis b. The line y = 1

Q: Find the point P on the graph of the function y = √ closest to the point (10,0) The a coordinate of…

A: Given, the curve is y = √x           --- (1) We need to find point P ( let P (x,y) ) on function y =…

Q: Find the area of the region described. Make a graph of the region in question. The region is bounded…

A:

Q: The cost C'(x), where x is the number of miles driven, of renting a car for a day is $53 plus $0.65…

A: Given: The cost C(x), where x is the number of miles driven, of renting a car for a day is $53 plus…

Q: Find the indefinite integral. (Use C for the constant of integration.) [19+ (9 + x + 6ex) dx

A:

Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = [(1 + 9x)^4 − (5 − x)^2]^3

A:

Q: Use a change of variables or the table to evaluate the following definite integral. 0 0 S 3π 2 Зл 2…

A:

Q: Find the indefinite integral. (Remember to use absolute values where appropriate.) 3x² + 5 0.3x³ +…

A:

Q: Let f(x) = cosx and derive its Maclaurin Series, and find its interval of convergence.

A: We have to derive the Maclaurin series and interval of convergence for f(x) = cosx.

Q: 4 '6 6x√x + 1 dx

A: Evaluate the definite integral. ∫466xx+1dx

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. ㅠ x = 35…

A: we have given parametric curve x=35 cos3θ  and y=35 sin3θ

Q: Solutions for the red boxes please

A:

Q: y=(2√√x-3)(6-5x²)

A: y=2x-36-5x4

Q: Yes it is conservative but you are incorrect on the rest of it

A:

Q: F(x, y, z) = xzi + xj+yk S is the hemisphere x2 + y2 + z2 = 16, y ≥ 0, oriented in the direction of…

A:

Q: Use cylindrical coordinates to find the volume of the solid. Solid inside x² + y² + z² = 16 and…

A:

Q: Consider the following. f(x) = 2x - y 4 3 2 2 y=2x- 4 dx x² 6 ▸ 8 (a) Write the integral that…

A: The given function is y=2x-x24

Q: PROBLEM NUMBER 7 af² ª ³+1 Using n 6 approximate the value of - de using (a) the Midpoint Rule, (b)…

A: Evaluate the integral ∫171x3+1dx a) Midpoint rule b) Trapezoid rule  c) Simpson's rule

Q: 1) Consider the coordinate triple (3,-1,-5). a. Plot the point by hand. (Please draw a large enough…

A:

Q: Find the volume of the region bounded above by the paraboloid z = 2x² + 4y² and below by the square…

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: y= √(64-x2)  We have to evaluate volume of solid formed by revolving the region about y axis

Q: Find the equations of the xy, xz, and yz traces of the function z = 4 - 2x² - 1². The xy-trace is:…

A:

Q: 7. Find real numbers a, b, and c so that the graph of the function yax2+bx+c contains the points…

A:

Q: Use Euler's method with step size 0.1 to construct a table of approximate values for the solution of…

A: we have   x0=0   ,    y0=1            h=0.1 ,          f(x,y)=x+y   y1=y0+hf(x0,y0)    = 1+0.1(0+1)…

Q: PROBLEM NUMBER 17 ●fe-et- Evaluate e-t 4 dt..

A:

Q: Let a= (3, -10,7) and b = (9, -2, 10). Compute the projection of a onto band the vector component of…

A:

Q: Compute the indicated derivative using the chain rule. y = u3, u = x − 6;  dy dx

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A:

Q: The equation below gives parametric equations and parameter intervals for the motion of a particle…

A:

Q: Find the derivative of the function. f'(x) = f(x) = x sin(2x)

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: The volume formula is

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. (a) (b) 2 0 y…

A:

Q: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

A:

Q: Sketch the graph of the following function 0 f(t) sin t 0≤t<π/2 π/2 ≤t≤T period ㅠ

A:

Q: Evaluate the triple iterated integral. *π/4 LLL 0 Jo '7 (7-r rz dz dr de

A: The triple integral is given by ∫0π4∫07∫07-rrz dz dr dθ To determine: The solution of the integral.

Q: Write the sum without using sigma notation. n Σ(-1)² + 2x³² j = 1

A: Summation means  Putting j=1,2,3.......n

Q: Lake Cachuma is stocked with 2000 rainbow trout, and after 1 year the population has grown to 4500.…

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A:

Q: = 1 VX dt It = 1

A:

Q: Solve given Linear Differential Equation Q4.5

A: To solve the following

Q: Please help with # 14 thanks

A: To solve the following

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

A:

Q: Given the function g(x) = 8x³ − 60x² + 144x, find the first derivative, g'(x). g'(x) Notice that…

A:

Q: Five years ago, you acquired a 30-year loan of $130,850, charging 6.5% annual interest, compounded…

A: we have to need two formulas. They are:

Q: π Find the arclength of the curve x = 7 cos(2t), y = 7 sin(2t) with 0 ≤ t ≤ 12 Submit Question

A:

Q: Find f such that f'(x) = 5x² + 9x - 9 and f(0) = 3. f(x) =

A:

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: Solve the initial value problem. 1 x + 1 y' + y = x=², y(1) = 2

A:

Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

A:

Q: Find the area of the region that lies above the x-axis, below the curve I = t²+2t +9, y=et with 0…

A: The given curve is:x(t)=t2+2t+9,    y(t)=e-t       with  0≤t≤1

Q: Find the area of the region inside: r = 9 sin but outside: r = 2

A: