1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves. Hence, find the area of the region shaded.

Q: Use implicit ?х ਹੈ: ду = = x + y2 + z? = 6xyz 6- 6x differentiation to find əz/ax and Oz/dy. 6- 2y

A:

Q: Find y" of y=- y" = y" = O y" = y" = X-1 2 (x-1)² 2 (x - 1)³ 1 (x - 1)³ -2 (x - 1)³

A: Topic = Derivative

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00).…

A:

Q: Use Newton's method with the specified initial approximation x₁ to find x3, the third approximation…

A: Given equation:- x5-x-5=0 , x1=1

Q: Solve the following system of equations. 3x+4y = 4 6x+4y = 16

A:

Q: Find the general solution of the given higher-order differential equation. y"" - 7y" + 8y' + 16y = 0…

A:

Q: Find the radius and interval of convergence of the power series 】 (−1)” (x+3)” √2n n=1

A: This is a problem related to series and sum calculation. Please follow the procedure given below.

Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co).…

A:

Q: 16-1

A:

Q: Find the equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

Q: Find the general solution of the given higher-order differential equation. y"" - 2y" - 3y' = 0 y(x)…

A:

Q: ow many values of a are there such that lim h→0 (sin ¹(a+h)-sin h ~ ²² (a)) = = 4?

A:

Q: 8 -6 4 수 +

A:

Q: Solve the differential equation by variation of parameters. -t y" + 2y' + y = et In(t) y(t) =

A:

Q: ssume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

A:

Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

A:

Q: Estimate the slope of the graph at the points (x₁, y₁) and (x2, Y₂). At (x₁, y₁), slope At (x, y₂),…

A: We know:- sllope of a line passing through two points =y2-y1x2-x1

Q: Evaluate the iterated integral. •π/2 [y/6 [5/y } 0 sin y dz dx dy

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given solution, y=c1cos3x+c2sin3x So, y'=-3c1sin3x+3c2cos3x So, y"= -9c1cos3x -9c2sin3x

Q: Divide. (8x³-4x²-12x+15) + (2x-2) Your answer should give the quotient and the remainder. Quotient:…

A: Please see the below picture for detailed solution.

Q: Identify the type of solution for the problem and solve for the general equation

A:

Q: Use Res(f(z), zo) lim (z-zo)f(z), Res (f(z), zo) = 2-20 to find the residue at each pole of the…

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Evaluate I= I=S 2+41 Iti NJ Z 2 dz

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

Q: The answer for x is correct but the answer for dy is wrong.

A:

Q: Solve for a in the triple integral. (Enter your answers as a comma-separated list. f3-a-y2 ↑4-x-y dz…

A: ∫01∫03-a-y2∫a4-x-y2dzdxdy = 14/15 here we have to find value of a  so integrate this and after  put…

Q: *T/2 10 cos(0) r dr de

A:

Q: Use the indicated change of variables to evaluate the double integral. 56xy dA x = 1/2 (u + v) y =…

A:

Q: Əw Find Ət using the appropriate Chain Rule for w = x² + y² + z² where x = 10rsin(s), y = 10tcos(s),…

A:

Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

Q: Describe a plane vector a. Sketch the vector PQ in the plane from initial point P(1, 2) to terminal…

A:

Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: Write the vector shown above in component form. Vector = Note: In the graph, each box is 1 unit by 1…

A:

Q: 4. (x-1)(2x³+2x²+3x+2) dx x³ (x+1) r 5. csc ³0 de

A: We have to integrate question no 4 and 5.

Q: Assume that the radius r of the cylinder below is decreasing at a rate of 2 m/s, and that its height…

A:

Q: Find the general solution of the differential equation y" - 2y + y = 7et 1+t2 NOTE: Use C₁ and C₂ as…

A: Given the differential equation is y''-2y'+y = 7et1+t2

Q: x, y) u, v) S S u area of the ellipse using the indicated change of variables. 1 V S S 2 u u

A:

Q: Find the derivative of the function using Chain Rule. Given f(x)=(x²+x-3)√√x²+x-3

A:

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A: Solution: Given: 2x - 5z =5 .............(1) 2x - 5z =6 .............(2) On solving both equations…

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(5,…

A:

Q: Given polar curves A₁: r = 1 + sin 0 and A₂: r = 3 sin 0 1. Solve for the polar coordinates of the…

A:

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: A  force 540 Newton stretches 3 meters .a mass of 45 kg  is atteched to the end of the spring and is…

Q: Find symmetric equations of the normal line to the surface 3xy-z = 0 at the point (-4, -2, 24). O…

A:

Q: Evaluate the iterated integral. π/4 ** ['y cos(x) dy dx

A: Please see the below picture for detailed solution.

Q: Find all x-intercepts and y-intercepts of the graph of the function. f(x) = 2x³ + 12x² + 16x If…

A:

Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing. show…

A: Topic = Functions

Q: =S • I = dx (x²+9²)² 2 ans ? tr 493

A: This is a problem related to integral solving using residual theorem. Please follow the procedure…

Q: Find the derivative of f (x) = 30 6/2x+1

A: Given problem:- f(x)=-302x+16  TO Find:- Deriative of f(x)