Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

Q: 3. Find the gradient of the function and the maximum value of the directional derivative at the…

A: As per our guidelines,we are supposed to answer only one asked question.So kindly repost other…

Q: A function has a tangential gradient of 2sin3x. If the curve cuts the x-axis at, determine the…

A: A function has a tangential gradient  of 2 sin 3x.If the curve cuts the  x-axis at π3.To determine…

Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not…

A:

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

A:

Q: Determine the critical points of f(x, y) = 4.xy-a -y". Then, using the Second Derivative Test,…

A:

Q: 3. (D - 3D? + 4)y = 40cos2x + 6

A:

Q: (b) Apply the First Derivative Test to identify the relative extrema. (x, y) = ( ,1 2 relative…

A:

Q: Find the rate of change of f(x,y) = In(x +y +z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: solve:

Q: What is the formula for the linearization of a function f at the point x = a? %3D

A: Given :To provide the formula for linearization of a function f at the point x=a

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

A:

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Solve using linearization using one digit approximation only 1) f(x) = V5

A:

Q: Estimate (2.4) by using a linear approximation of f(z) =x² about the value z 2. %3D Round your…

A: We have to find

Q: Use centered difference approximations to estimate the first and second derivatives of y = ex at x =…

A: The central difference for first and second derivative is calculated respectively,

Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: How does Taylor’s formula for a function ƒ(x, y) generate polyno-mial approximations and error…

A:

Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: The partial derivative of function respect to y* f(x, y) = x² + y/y? %3D

A:

Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

A:

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

A: Topic- Vectro

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

A:

Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

A:

Q: Does Newton’s Method fail when the initial guess is a relative maximum of f ? Explain.

A:

Q: The directional derivative of f(x, y) (3, 4) is -In(x² + y²) at the point P(1, 5) in the direction v…

A: Definition used -          Directional derivative at the point -     The rate of change of f(x, y)…

Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

A:

Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

Q: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

A:

Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. (3.97) =

A:

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: Find the maximum value of the directional derivative of the function f(x, y) = tan at the point…

A:

Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

A:

Q: Classify the point (1, 1) for f(z, y) = zye" 2 by using Second derivative test if POSSIBLE. Lütfen…

A: Given that,                  fx,y = xye-x2-y22 . We have to classify the point 1 , 1 for fx,y by…

Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: Find the rate of change of f(x,y) = In(x +y+ z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: Given problem is :

Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…

A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)

Q: +y a) Find the critical point(s) of f(x, y). b) Use the second derivative test to classify the…

A:

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

A:

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. (1.97) =

A:

Q: Find the linearization of f(x, y, z) = 2 centered at (1,3, 2). Use it to estimate f(1.01,3.01,…

A: Given:fx,y,z=xyzTo find a)The linearization of f centered at 1,3,2b) use a to estimate…

Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

Q: Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in…

A: Given thta  f(x,y,z)=x/y+y/z+z/x  To find teh derivative of the function at point p in the direction…