+*=1 are The vertices of the ellipse given by (2, 1) and (1, 2) (0, 1) and (0, – 1) Option 1 Option 2 (-2, 0) and (2, 0) (2, 1) and (-2, 1) Option 3 Option 4

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

Q: Find and sketch the domain for the function. foxy) = - 25) ( - 4) Find the domain of the function.…

A: function f(x,y)=(x2-25)(y2-4)

Q: Let B be the sphere x2 + y? + z? = 1. The volume of the portion of B contained in the first octant…

A: Given : B be the sphere x2+y2+z2=1

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: What are the two values of k closest to -7 for which , sin2 (x +7)- cos2(x +7) da has a value of 12…

A:

Q: dy By using implicit differentiation, find dx x.y)-(1.0) for xy + e*» = sin(x +1). (x.y)-(1,0)

A:

Q: Evaluate the following integrals i. L Ix| e(1+x*) dx -0.5 ii. So x cosh(x² + 1) dx

A:

Q: Create a function where the domain is not a set of numbers and the range would be the set of whole…

A:

Q: (b) w = x²y – 10y2²2³ + 43z – 7 tan(4y) dw 2xy + 43 z² – 20yz³ – 28sec² (4) dy –30y²2² dz %3! dz

A:

Q: aluate the function. Give the exact value. cos tan(V3) -1 cos(arctan( V3% = 0.5

A: Given query is to find the value of the expression.

Q: Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

A:

Q: 1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R…

A: Given

Q: dz dz and ду IV. Suppose z is a function of x and y, and tan Vy? + x² = z"e©y. Solve for

A: We have to Solve as per given conditions.

Q: 1. Find the total differential dw. 2. w = re2u +e-V

A:

Q: 7x – 2r – 12 For the function f(x) =- x² +6 a) Find the equation of the non-vertical asymptote b)…

A:

Q: Using Laplace transform to solve the IVP: y" – 9y = e *, y(0) = 0, /(0) = 0 %3D we find the solution…

A: The given IVP is y''-9y =e-3t,   y(0) =0, y'(0) =0 To solve the problem we must know the following…

Q: Let W = (a + bxr +x? € P: a,b ER) with the standard operations in P2. %3D Which of the following…

A: W is not a subspace of P2 because 0 does not belong in W.

Q: Solve the equation on the interval 0 s0< 2n. 2 sin 0 + 1 =0

A:

Q: the second order partial derivatives of the given function. (x.y) = xye -y O A. 21 = 0;=2xye -Y (2y²…

A:

Q: Determine the sum of this convergent series.

A: This question can be solved using the concept of infinite geometric progression.

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

Q: Determine any critical point(s) for the function f(x)=-3x2-9

A: For Critical Points We will Put F'(x)=0

Q: By considering different paths of approach, show that the function below has no limit as…

A:

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: C hnd the hrst order parha derivve f(x,4,2)= W = e 32 *y-16y²23 + 43x 4.5 %3D %3D h Cs, t) = ° t*In…

A: We will find the partial derivative.

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: 1. Evaluate the following integrals. 24 - 44 dy 2+ 49 C.

A:

Q: The series 1 + Vn? 1+ Vna 00 n=1 is convergent if and only if: Select one: 72 a > Ob. 35 a * 35 4 O…

A:

Q: What are intervals of concavity of the function f(x) = -2x – 6x² – 3 ? a. Concave upward on (-o, 1)…

A: Concept: Concavity: If the line connecting two points is above the graph, or if the first derivative…

Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: Find the linearization L(x,y) of the function f(x,y) = e 4x cos (7y) at the points (0,0) and 0,- ...…

A: To find the linearization Lx, y of the function fx, y=e4x cos7y at the the points0, 0 and 0, π2.

Q: Curve Sketching Sketch the graph of the following function: f(x) = 3x3 + 2x2 - 4x + 2

A: We have to draw the graph of given function

Q: 프-3r-dx= a) 클m3x + 21+ tanx + C b)습 미3x + 21-tan'x + C Q13:J +1)(3r+2) d)흘 I미3x + 21+ tanx + C -1…

A: The integration of the integral is  (2x2-3x) /[(x2+1)(3x+2)].

Q: Given f(x) = (2x - 3)" (x+1). Determine (if any)

A: Given

Q: z-1 Suppose the symmetric equations of lines l4 and l, are = 2 – y = z and x = -1, = 2 respectively.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Question 3 Compute V31.6 approximately by use of differentials. 1.098 (E) None of the choices 1.890…

A: 31.65=1.995

Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

A:

Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: -2 is a critical number of the function f(x) = /2x – x². - Select one: O True O False

A:

Q: Rationalize the denominator. Vx - 9 6/x

A:

Q: 24 – 49 dy 2+ 49 с.

A:

Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = - 3 ex cos (yz),…

A:

Q: etermine whether the series E converges or diverges. If it converges, find its sum. m= 2 elect the…

A: Given query is to find series converges or diverges.

Q: If the 6th term of an arithmetic sequence is 63 and the 14th term is 135, write the formula for the…

A:

Q: 1. Evaluate the following integrals. | (csc 0)(1 + sin² 0 + sin 0 cot? 0) de а.

A: Given ∫(cscθ)(1+sin2θ+sinθcot2θ) dθTo evaluate the integral:

Q: dy + 7z = 5 5 – 72

A:

Q: derivative(y

A:

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: Sólvé thé équátión ón the interval U30<2T. 0<2x. 4 sin 0 + 5 = 7

A: