Give a parametric representation for the path followed by a heat seeking particle placed at point P on a plate if the temperature field of the plate is given by T(5x). |Change (y' to y² ). T(x, y) = 64–x² – y P(4,2)

Q: Let h be a differentiable function of z obtained from the parametric equations z = f(t), y = 9(t).…

A: Option  1  is true .

Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

A:

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

A:

Q: 5. x² +7y° For the function f(x,y)= x° find f, fy, f,(-5,-4), and f (0.-2). + y

A:

Q: Question: Find Y As A Function Of T If 16y" - 40y' + 25y = 0. Y(0) = 9, Y')O) = 5. Y = . Find y as a…

A:

Q: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

A:

Q: Determine the order of the DE. a.) y' + y = 5y^2 b.) (dy)/(dt) = t c.) y' = y'' + 5t^2

A:

Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

A:

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: Find the He Intertl Of Colvergelke HON e raus and Couverge (3x-1)" 12+h

A:

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Use implicit differentiation to find dy/dx and d²y/dx². xy + 3 = y, at the point (4, -1) Select one:…

A: According to guidelines I can solve only 1st question

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: apply shifting property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: To apply the shifting property of Laplace in the given equations.

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum rate of change of a function f(x,y)�(�,�,�) occurs in the direction of the gradient…

Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

A:

Q: a) Describe the curve obtained when we make y = 2 and 2= √2 a f b) Represent on this curve the…

A: Given That : y=2 and z=2 To Find : a) Describe the Curve obtained when y=2 and z=2 b) Represent on…

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

A:

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: f(x, y) = xsin²y + y² cosx, Find fxy a. sin² y - y² cosx b. 2xsinycosy-2ysinxcosy c. 2sinycosy -…

A: We need to find fxy.

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

A:

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00