(i) Find all first and second order partial derivatives of f(x, y) = x²y + cos(xy) (ii) Find lim xy² (x,y)→(0,0) x³ + y³ if the limit exists. If it does not exist, explain why.

Q: 품 tan (2x) sec² (2x)dr

A:

Q: Compute the gradient of the following function and evaluate it at the given point P.…

A:

Q: 1. Given r(t) = <In(cost), -1, 2 $₁ 2 A a) Find the length of the curve for r(t) at 0<t< R|4 b) Find…

A:

Q: What is the radius of convergence of a power series? How do you find it?

A: Here we have to define the what is radius of convergence and interval of convergence and how to find…

Q: use the if f₁ (t) properties of Fourier transform ē at ult) = JF.T =jº f(t) = ³wt dt 88 Seat, ejut…

A:

Q: 6. Write down the partial differential equations for; (a) Diffusion equation (b) Wave equation,…

A: Diffusion equation identical to heat equation  Wave and Diffusion equation contains partial…

Q: 1 4r dr √1-4

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

A: Find complementary solution  Then find wronskian of the functions which are solution of homogeneous…

Q: Determine the general solution of the given differential equation. y"" - y" - y + y = 3et+2 NOTE:…

A:

Q: Take xlt) then x (1) = => x/w) = -jut J'est dt 1.e => x(w) == 1 JW X(w) = Lx -jwt ax e [f10+ ] ~ Sex…

A: To check the +ve or -ve

Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: -if f₁ (t) properties of Fourier transfor eat alt) JF.T = $ fit) ējut dt = - feat. ejust dt е ماز-…

A: Topic:- calculus

Q: Use the table to find lim f(x) z 3 X 2 2.9 2.99 3 3.01 3.1 4 f(x) 6 7.8 7.99 7 8.02 8.1 11

A: Topic:- application of calculus

Q: The general solution of xdy-ydx = x²e³dx is (Α) y+x² +cx=0 (В x+ye-cx=0 Ⓒ D yamcx=0 x-ye+cx=0

A:

Q: The gradient at (-2,1) is

A:

Q: Let 8 f(x) = ΣX2 n = 1 Find the intervals of convergence for f. (Enter your answers using interval…

A:

Q: Determine the general solution of the given differential equation. y"" - y" - y + y = 5e-t + 2 NOTE:…

A:

Q: Find the vector component of v = (4,-1,7) along b = (4,4,-7) and the vector component of v…

A:

Q: Write the row vectors and the column vectors of the matrix. 311] -404 (a) the row vectors (b) the…

A:

Q: The indicated function y₁(x) is a solution of the given differential equation. xy" + y' = 0; Y₁ =…

A:

Q: 5x^4-8x^3+6x-5 find the second derivative and find the concavity upward and downward

A:

Q: The general solution of (3tanx-2cosy) sec²xdx + tanx sinydy=0 by Substitution i A B C D tan ²x…

A: To find general solution of given differential  equation.

Q: 7. Let f(x, y) = a) xsin y-y sin x + y find Simplify and give exact value b) 0. Simplify and give…

A:

Q: The DE of the family of circles with center at the origin is

A: The general equation of circle centered at  orgin with radius r is (x-0)2+(y-0)2=r2

Q: Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that…

A: The given data is: Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min To find: How…

Q: 2x-√5+4x lim x→6 x-3

A: The given limit is limx→62x-5+4xx-3

Q: Find the area of the region common to the interiors of the cardioids r= 1 - sin 0 and r= 1 + cos 0.…

A:

Q: Consider the graph of distances from the origin as a function of time for a car trip. 150+ 100…

A: We have given graph of distance vs time.

Q: 1 Defennire it the following series is Convergent divergent. E n=1 3 ²+2

A: since multiple questions are asked, I am answering first question

Q: The derivative with respect to x of the function sec y where y sec¹(2* cot¹x) is

A: We can solve this as follows:

Q: Find the divergence of the field. 2xyzk F = 5ye 2xyzi + 5z e 2xyzj+5x e² div F =

A: Solve the following

Q: Evaluate the iterated integral below. π 1 4 S*S'y cos (x) dy dx Só 0

A:

Q: Find the solution of the given initial value problem: y(4) + 2y""+y" + 8y′ − 12y = 6 sin(t) + 80e¯t;…

A:

Q: ℗ Solve the following ODES by Undetermined Coeff. в +у= y-2y +y = esinx Ans: y = ₁₂e + ₂ xe - è sin…

A: As per the rules we can answer only the first question and rest can be reposted.

Q: Differentiate each function. f(t)=sin5t

A: We have to find derivative

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

A:

Q: Find the gradient vector field of f. f(x, y) = xe³xy Vf(x, y) =

A:

Q: Compute the gradient of the following function and evaluate it at the given point P.…

A: Given the function  g(x,y)=x2-4x2y-5xy2 ; P-2,1

Q: Evaluate the iterated integral below. π/4 1 S. S'y co Só 0 0 y cos (x) dy dx

A: Solution…

Q: 2.) Sketch the region in the plane consisting of all points whose polar coordinates (r, 0) satisfy…

A:

Q: You are planning to make an open rectangular box from a 31-in.-by-61-in piece of cardboard by…

A: First take a square of length x then make a box and find the volume in terms of box . And…

Q: Exercise 17. Compute the following integrals 1 (a) -dx 2 sin² x + sin x cos x cos²x (b) -d.x 2 + tan…

A:

Q: Solve the differential equation by variation of parameters. 4y"8y' + 8y = ex sec x y(x) =

A:

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: f(x) = log5 (2x + 1).

A:

Q: or the graph below, identify a restricted domain for which the function has an -2 YA 8- 2- 0 -2- 2 6…

A: Topic:- calculus    Definition :-  The domain of a function f(x) is the set of all values for which…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

A:

Q: The life X, in hours, of a certain kind of electronic component has a probability distribution…

A:

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

A: