Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, - 2), (0.2); vertices: (0, - 6). (0,6) Type the standard form of the equation. 2 (Type an equation. Simplify your answer.)

Q: Given a = 3 units, = 1 unit and the angle between a and b is 30°, determine o) the exact value of (…

A: Solution:

Q: Complete the following steps for the given function. a. Use polynomial long division to find the…

A:

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n5 +…

A: Use alternating series test for checking the convergence of series .

Q: Summation of n = 0 to infinity of (x3n) / (n!) Find radius and interval of convergence.

A:

Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 1 + 8 1 + +... p =…

A:

Q: dx xV4-x?

A: Explained below

Q: 4. Use partial fraction decomposition to evaluate dx x' + 4x +3 2

A:

Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: S- 3 dy 3y - sin n -1 4-9y2 3 A True B False

A: We have to find out

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A:

Q: x³dx U sing trigonometric substitution, is equivalent to

A:

Q: The number N of beavers in a given area after x years can be approximated by the following. N = 5.5…

A: Given  population of beavers in a given area after x area N=5.5×100.23x    ,  0≤x≤10

Q: An antiderivative for is: 22 +81+20 1 O In + C I+8 ㅇ 올tan-1 () +C 금i미플의 O In 28|+ C O tsec- (4) + C

A:

Q: Find the exact value of the expressions cos(a + B), sin(a + P) and tan(a + B) under the following…

A:

Q: f(1) 100 g(x) lim where f(r) and g(x) are seen in the graph.

A:

Q: For the function f(x) ex x>0 a) Determine the coordinates of all critical points. b) Use the first…

A:

Q: Use substitution to find the Taylor series at x 0 of the function 4 sin (-x). Choose the correct…

A:

Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

A:

Q: Complete parts a through c for the given function. f(x) = 4x° - 5x - 40x° + 5 on [-3,4] a. Locate…

A: Given problem:- f(x) =  4x5 -5x4 -40x3 +5 To find:- a). Critical points  b) Use the First Derivative…

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y = 9 and…

A:

Q: Which of the following is NOT a correct way to express the vector v = (2,-4) %3D a) 2î - 4 where î =…

A:

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

Q: A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long…

A: see below the answer and explanation

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A:

Q: Jy csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соѓу+ coty dy D) None E у…

A:

Q: Find the magnitude Iv|| and the direction angle 0 for the given vector v. v= - 7i+ 10j ... (Round to…

A:

Q: Find V (F × G), if F(x, y, z) = 11xi+j+3yk and G(x, y, z) = xi + yj – zk. V. (F x G) = %3D

A:

Q: an best be evalu er Formula nometric Transf nometric Formu

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

Q: 5. J 12 csc (-6х) cot (-6x) dx 6. J2x3 cot х4 dx 7. S xª sec (x5 - 9) dx 8. S tan 3 x dx

A: The given integral are 5) 12 csc(-6x) cot(-6x)  6) 2x3 cot(x4)

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

A:

Q: Find the area of the plane region bounded by y = x3, x = -2 and x = 2.

A:

Q: . .............. Solve the exponential equation algebraically. Approximate the result to three…

A:

Q: Determine if the following functions are odd, even, or neither. Provide reason. (a) f(x) = x² (b)…

A:

Q: Find V · (F × G), if F(x, y, z) = 3ri+j+6yk and G(x, y, z) = xi+ yj – zk. V· (F × G) ||

A:

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.

Q: nd the volume of the solid generated by

A:

Q: Find the area of the plane region bounded by y = x - 4x and y% x(2-x). Answer

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A:

Q: Consider the initial value problem. y'' − y' = ex,              y(0)=0,   y'(0)=0 (a) Write the…

A:

Q: Suppose f(x) = x² – 10x + 1. Compute the following: - A.) f( – 2) + f(4) = B.) f( – 2) – f(4) = -

A: Given query is to find indicated function value.

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

A:

Q: es conve n=1

A:

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: Suppose a population function P(t)  the following differential equation. P is measured in millions…

A: Given dPdt = P(P-10) The slope field is plotted in Desmos slope field generator

Q: Find the first four terms of the binomial series for the given function. -2 1+ 10 OA 1-맛+ 100 250 1…

A:

Q: Determine the following limit at infinity. lim (- 12x-8) Select the correct choice below and, if…

A:

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: S- (1+x²) = x*dx Using trigonometric substitution, tan ode A sece sin Ode B cose S tan od0 sec20 sec…

A:

Q: The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3y* = 0. a) Calculate the value of p.…

A: Since point , P(p,1) lies on the given curve, therefore this point will satisfy the curve .Using…