af af дх ду дх (1, -1) and Of ay l(1, -1) af Calculate when defined. (If an answer is undefined, enter UNDEFINED.) f(x, y) = e0.5xy af af ду Round your answers to 4 decimal places. af дх (1, -1) af ây (1, -1)

Q: Find y(0.2) for y"=xz²-y², xo=0,yo-1,20-0, with step length 0.2 using Runge-Kutta 2 method (2nd…

A: To find- Find y0.2 for y'' = xz2 - y2, x0 = 0, y0 = 1, z0 = 0, with step length 0.2 using…

Q: If z=(X+Y) e and X-u * find the tollawing partial derivatives using Chain ruleo Express answers as…

A: Given, z=x+yeyx=u2+v2y=u2-v2 To find : ∂z∂u , ∂z∂v

Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: Find the simplified form of the derivative of y = 1+csc 3x %3D cot 3x O y = 3 csc 3x csc(3r)-1 O (E)…

A: We have to find the simplified form of the derivative of  y = 1+csc 3xcot 3x.

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

A:

Q: Evaluate the derivative of z f8.png asin (bvx3) f(x): %3D c2x + In(kx) if a = 15.08, b = 5, c = 5,…

A:

Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: 18. If u = [13,7,-2] is orthogonal to v--5,k,7], d A mine the value(s) of k %3D %3D 19. Find the…

A:

Q: Given f(x,y)=3.xy² -2y+5x²y° . (i) Compute the first order derivatives f, (x, y) and f,(x,y)· (ii)…

A: Given function is  f(x,y)=3xy2-2y+5x2y2

Q: 7. Suppose that x and y are related by the equation x 2−4y 2=5 and use implicit differentiation…

A:

Q: Use a linear approximation (or differentials) to estimate the given number. V 99.4

A:

Q: 5) Starting from the expression Cp- Cy = T use the appropriate relations between partial derivatives…

A: The amount of heat required to raise the temperature by one degree in one mole of the substance is…

Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

Q: Suppose that f(x, y) the point (x, y) = (2, – 6) is = xy. The directional derivative of f(x, y) in…

A:

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: 5) Find the gradient of o = x?yz + 4xz2 at (1, -2, -1).

A:

Q: Find the differential of the function. y = (5 - v^2) / (5 + v^2)

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: Use a linear approximation (or differentials) to estimate the given number. (8.09)2/3

A:

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: stlon 5 Use differential to approximate the change in the value of f(x)= ° as e goes from 2 to %3D…

A:

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

A:

Q: 2 If 3x? + 4x + xy = 1 and y(1) = - 6, find y'(1) by implicit differentiation.

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Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

A:

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: Evaluate the value of ‘a’ if the first derivative of m(x,y,z)=4-ax^2-2y^2, with respect to the…

A: Consider: mx,y,z=4-ax2-2y2 and mx1,2,3=-2. Solve for a. Calculate mxx,y,z by applying…

Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

A: Given:- f(x)=x4sin(9x+12)+ln4x+10x3 To find:- Derivative of given function

Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

A:

Q: Q14. If V = f(2x – 3y,3y- 4z,4z – 2x) then apply chain rule of partial derivatives to prove that 6-…

A:

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

A:

Q: C(0) = 1000 and C'(x) = 400e^(-0.1q) + 8.  Then C(x) is A.  -4000e^(-0.1q) + 8q + 1000 B.…

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Q: az (8) Find variables z and y and partial derivative exists. if the equation yz – In z = x² +y?…

A:

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: af and дх if f(x,y) = 3x* – 5x²y + 3xy3 + Find %3| ду se sin xy2. x+2y Find the partial derivative…

A: Partial differential equations

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.

Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.