Find a function r(t) for the line passing through the points P(0,0,0) and Q(1,6,2). Express your answer in terms of i, j, and k. r(t) = ti + (Dj+ (O K, for

Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: Find y as a function of t if 9y" +12y + 29y = 0,

A: 9y''+12y'+29y=0which condition y(2)=8, y'(2)=9To Find: y(t)

Q: Find the linear approximation of the function f (x, y) = 2x – y+x?y - near the point (2,0). O 2x +…

A:

Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

A:

Q: Find the linear approximation of the function f(x) = Vx+3 at a = 1 and use it to approximate the…

A: Given the function fx=x+3. Find the linear approximation of f(x) at a=1 and use it to approximate…

Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96,…

A:

Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

Q: Differentiate the function. y = In(16 + t – P) %3D y' = 1– 3r² 372 6 +t-t -- 6 + t- r 2 6+t-t

A:

Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

A:

Q: Find a function r(t) for the line passing through the points P(0,0,0) and Q(4,2,1). Express your…

A:

Q: Find the function r that satisfies the given condition; r' (t) = i+ te-tj-4k;r(0) = i+ t2+1 - 3k

A: Given problem:-

Q: Find the local linear approximation of the function f(x) = V1 + x at xo = 3, and use it to…

A:

Q: Determine the linear approximation of f(x) = x' at x = 1. O a. Not in the list O b. y=- 9 x -8 O c.…

A:

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Find y as a function of t if 5y′′+31y=0 y(0)=4,y′(0)=7y(t)=

A: The given differential equation is  5y''+31y=0   ......(1) and the initial condition is y(0)=4 and…

Q: Find the linear approximation to the equation f(x, y) = 3, xy at the point (8, 4, 6), and use it to…

A: To find the linear approximation to the equation at point (8,4) Given that f(x,y)=3√(xy)/8

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: Find a function r(t) for the line passing through the points P(0,0,0) and Q(2,4,8). Express your…

A: Given P (0,0,0) , Q ( 2,4,8)  Find  r(t)

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: For the function f(x.y,z) = 1 + xy - 5z*, find fy, fy, and f,. fx -ロ fy = =ロ

A:

Q: Find the linear approximation of the function f(x) = v9+x at xo = 0, and use it to approximate v8.9…

A:

Q: Q2: Find ôf ôf - for the function f(x, y, z) = x²y+ y° + xz² and Əx 'dy

A: We will find out the required values.

Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

A:

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

A:

Q: Determine the linear approximation of f(x) = at z = 1. O a. y= 9x +8 O b. y=- 9 x-8 O c.y = 9x - 8 O…

A:

Q: function f(x, y) = 2x^3 + 6xy^2 −3y^3 −150x has four stationary points, find

A: Please refer to the image below

Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: (a)

Q: Given f(x,y) = sqrt(x^2+4y^2) at point (3,2) find the linearization and use it to approximate…

A:

Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: For the function f(x,y,z) = 1 + xy“ - 2z*, find fy, fy, and f,. fx f2

A:

Q: Find the linear approximation of the function f(x)= cuberoot(1+x) centered at 0. Use this to…

A: For the solution follow the next step.

Q: Consider the function: f(x,y) = 5xy - 7x² - y² + 3y, (a) Given that x = 6±0.6 and y=9±0.7, calculate…

A: As per the question we are given the following bivariate function : f(x,y) = 5xy - 7x2 - y2 + 3y And…

Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

A:

Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: Find the linear approximation to the equation f(x, y) xy at the point (4,8,4), and use it to…

A:

Q: Find z'(t), where z = In (x + y), x = 2t e', and y = 5e', in the following ways. a. Replace x and y…

A: follow next step

Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

A:

Q: For the function f(a, y) = wy - 2, we have f(2, -1) = -6. Use a linear approximation to estimate…

A: Solution of given problem is given as:

Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

A:

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

A:

Q: Under what conditions is a linear function f(x)=mx+b,m≠0, a linear function?

A: Here I am attaching image so that you understand each and every step.

Q: Find the local linear approximation of the function f(x) = V1 + x at xo = 3, and use it to…

A:

Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

Q: Find y as a function of t if y(t) y" + 2y + 10y = 0, y(0) = 8, y'(0) = 9.

A: The given DE is: y''+2y'+10y=0 The auxiliary equation of the given DE is:…