3 Find the center of mass of a thin plate of constant density & covering the region bounded by the parabola y = x² The center of mass is located at (x, y) = (Simplify your answer. Type an ordered pair.) and the line y = 6.

Q: For the function f(x.y.z) = sin'(5xyz), find fy. fy. and f (Type an exact answer, using radicals as…

A: f(x,y,z) = sin-(5xyz) fx = derivative with respect to x fx = 5yz/1-25x2y2z2 fy = 5xz/1-25x2y2z2 fz =…

Q: Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³

A: Given function: fx=3x4-4x3

Q: 17. DETAILS MY NOTES Consider the function below. (If an answer does not exist, enter DNE.) f(x) =…

A:

Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine…

A: Option (B) Diverges

Q: af af Find and for the following function. ?x ду 9xy In (5y) f(x,y) = e af ?х II

A:

Q: 4. Find the partial fraction decomposition of 1 x2 + 2x - 8

A:

Q: Find the slope, m, of the equation of the tangent line to the graph of y= (2x + 1)e* at the point…

A: derivative

Q: Life Expectancy of a Female Suppose that in a certain country the life expectancy at birth of a…

A: In order to get g(t) integration need to be done.

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: Let u = (– 2, 4, 0) and v = (– 1,0, – 3). Find the angle 0 <0 < 180° (in degrees) between u and v.…

A:

Q: 5元 3) 3 S元 6. 0- 7元 11元 6. 6. 4元 3 元一6 3. R一3 2. 如一2 R一2 3. 与一3

A: Given polar coordinate is 2,5π3. Choose the circle with radius 2 and then the given angle.  The blue…

Q: Find the volume of the solid generated by revolving about the y-axis the region bounded by the given…

A: First we should recognise the small volume dv and then integrate it between the appropriate limits.

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

A:

Q: A car leaves leaves the sa the first car at that insta

A: Here we have to find the rate at which the distance between the two cars is changing.

Q: Find the points of intersection of the graphs of the equations. 2+y = 18 -2x + y = 15 %3D %3D (х, у)…

A:

Q: A company selling widgets has found that the number of items sold z depends upon the price p at…

A: A company selling widgets has found that the number of items sold x depends upon the price p at…

Q: Let f(x) = 2log, (x) - f'(x) = ƒ' (1) =

A:

Q: Use the graph of g(x) to answer each question. O

A:

Q: Find what value of c does S da = 1? 4 Answer:

A:

Q: ah find and 3x + 8y For the function h(x,y) = 9ху - 1° ду dh dx

A:

Q: Find the length of the arc formed by ² = 10y³ from point A to point B, where A = (0,0) and B = (100,…

A: We can find the length of arc by applying length of arc formula.

Q: 1. Find the area bounded by: x=y² and y=-x²

A:

Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Given function F(x,y)=3x+2y Take path  Y=-x  X→1 then y→-1 Then function F(x)= 3x-2x=x

Q: Verify the divergence theorem for A = 2xyi -yz 2 j + xzk taken over the region bounded by x = 0, y…

A:

Q: 1. If f (x) = 5x – 6x2 + 4x - 2 find f'(x) and f'(2).

A:

Q: Identify the type of quadric surface defined by the equation 0, 2 4 and find all x-, y-, and…

A:

Q: Kindly solve the following completely within 20 minutes and draw thecomplete figure.    1. FIND…

A:

Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…

A:

Q: Notice that vector v shows a direct path from the initial 6. point (0,0) to the terminal point…

A: See this solution in below

Q: A fencing is limited to 50m length. What is the maximum rectangular area that can be fenced in using…

A: Recall:  Area of rectangle=length*breadth

Q: 2. Differentiate cach function. Simplify as much as possible and express all answers using positive…

A:

Q: 1. Find for each of the following: dx d) y = e +x* +e° g) y =x2r-5 h) y = log3

A:

Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: TQ two values of x such that 2x 1. 12x x+41 .a x-1/3 ,x=1 .b x=2, x=-2 .c x-3, x=-3 .d X=-1, x=1

A:

Q: A ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the…

A: We can find the rate of decrease of angle of elevation as below.

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

A:

Q: Match each function with its derivative. y dy dx ха X a. cos x b. In a • a* ✓ax C. sin x - ✓sin x d.…

A:

Q: Let f(x) = ln(x7) f'(x) = ƒ' (e²) =

A:

Q: Over the interval shown above, the associated marginal cost is... O Increasing, then decreasing O…

A: given

Q: Find the exact value. (a) sin( (b) arctan (-) (c) arccos (cos())

A:

Q: The matrix given is in reduced echelon form: 1  0  5  -2 0  1  4   1 0  0  0   0  Write the…

A: To write the matrix equations.

Q: 2) 1 V1-x² dx

A: The given integral,      ∫11-x2dx

Q: Hiws find the integral of the Pouction fix y1= over the region betwein the twe circles of rading 2…

A:

Q: Kindly solve the following completely within 20 minutes and draw the figure/graph for each,…

A:

Q: Determine the radius of convergence of the following power series. Then test the endpoints to…

A:

Q: Exercise 195 Further problems on Leibniz's theorem 8. If y = (x³ + 2x²)e2* determine an expansion…

A:

Q: Let f(t) Find the Laplace transform F(s) by computing the following integral: 00 [ f(t)e=" dt = […

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

Q: 5. If fx) = ene0", find f"(0). a. e b. 1 C. 7 d. 0

A: Derivative

Q: af ay f(x,y)=√√4x²+ +y² af Find and əx || (Type an exact answer, using radicals as needed.)

A:

Q: of and дх of Find for the following function. dy f(x.y) = (x' - 4) (8y + 7) of dx

A: To find ∂f∂x and ∂f∂y for the following function.fx, y=x5-48y+7