Find the area of the surface generated by revolving about the x-axis the ellipse x = acost, y = bsint. The eccentricity of the ellipse √²-b² is e = a 2лab а. 2лb² + - Arcsin e 2лab b. 2πb² + 2лab C. - Arcsin e d. 2πb²_²пab - Arcsin e e. NONE OF THE ABOVE A B D E

Q: dy dx = x+1 2(y+3)

A:

Q: II. Evaluate the following integrals. 2. (sin³x)√1 + cos x dx KIN k 플

A: Here is the solution:

Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Find the point on the line y = 4x closest to the point (1,0). (Use symbolic notation and fractions…

A:

Q: Let z=f(x,y) = 20x² 25xy + 16y². Find the following using the formal definition of the partial…

A: Given : z=f(x,y)=20x2-25xy+16y2   To Find : a) ∂z∂xb)∂z∂yc)∂z∂x(-1,1)d)fy(4,-1)

Q: As part of a chemical experiment, a scientist determines that the number sodium in a chemical…

A:

Q: Find I must find the indefinite integral then I need to use the result to calculate the definite…

A:

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y = 2x…

A:

Q: 3. Find the area bounded by a parabola and any right chord (use the parabola y2 = 4ax, chord x = x₁)…

A: In this question, we want to find the area bounded by the parabola and a right chord.

Q: - 6 = ₁6 -X

A:

Q: ¹In(1 + x) -dx X

A:

Q: Perform the integration. (sinh x)(coth? x + csch3x) dx

A: Here is the solution:

Q: quickly

A:

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the production for minimum average cost.

Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: Find the value of t 20 + 10t - 4.905€ ² =0

A:

Q: 2. Using power series, evaluate lim x → 0 sin x-x 3 X

A:

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

A:

Q: Evaluate ¹ dx √√9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

A:

Q: Question 1. Sketch the following regions in the xy-plane. Make sure to shade the region and label…

A: To sketch the given regions in xy plane.

Q: 00 ermine the converges or diverges of the series n=1 = 1 (n+1

A:

Q: 5.The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: Let's find two numbers & smallest possible value of sum of their squares.

Q: ind the absolute extremum values of f(x) = xe² on the interval [0, 1]. Note: e 0.22) ≈

A:

Q: Find the equation of the family of orthogonal trajectories of the system of parabolas y² = 2x + C.

A: Orthogonal trajectory

Q: Suppose that $2,500 is deposited into an account paying 6.2% interest compounded continuously.…

A: $2,500 is deposited into an account paying 6.2% interest compounded continuously.

Q: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: an = an-1/n

A:

Q: For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√92¹-1…

A: Topic = Derivative

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A:

Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

A: The given series   ∑n=1∞(-1)nn+3

Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…

Q: 2. I cosh ix dx

A:

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

A:

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A:

Q: 12. We have the following width measurements of 80 meters wide lake Distance: 0 10 20 30 40 50 60 70…

A:

Q: Evaluate f(x³ - x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

A:

Q: (b) lim *+1 √√2x+6-2 x²-1

A:

Q: True

A:

Q: The cost (in dollars) of manufacturing one item is given by C(x, y) = 10 + 9x + 7y where x is the…

A:

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A:

Q: (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a…

A:

Q: Find fx (x,y) and f, (x,y). Then find fx (2, -1) and fy(-4,3). f(x,y)= ex+y+5 fx(x,y)=

A:

Q: 4. (x³ − 2x² + 1)dx [³ (x² - 2x + 5)²

A: The integral to be evaluated is ∫x3-2x2+1dxx2-2x+52. The first step will be to do a partial fraction…

Q: Find all points where the given function has any local extrema. Identify any saddle points. f(x,y) =…

A:

Q: 3. Find f'(x) if f(x)= 3 2x + sin r

A:

Q: Let f(x) = e2sinz 1. Use the local linear approximation of f at x = 0 to approximate e2 sin(0.01

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…

Q: Evaluate ²(2x + 3e* - 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given problem:-