9. Use f(x, y) = Vx? + y? to give a linear approximation of v/3.12 + 3.992.

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

A:

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

A:

Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A:

Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

A:

Q: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

A:

Q: Let y = 5x? + 5a + 3. If Aæ = 0.3 at x = 4, use linear approximation to estimate Ay Ay = > Next…

A: Explanation of the answer is as follows

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

A:

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: Find the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

A:

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

A:

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: Let y = 5x + 7x + 3. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay =

A: Follow 2nd step.

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: Let y = 5x² + 8x + 4. If Ax = 0.4 at x = 2, use linear approximation to estimate Ay Ay a

A: By linear approximation we can write,       ∆y ≈ dy = f'(x) dx Also We have,          ∆y =…

Q: 5x + 6x + 2. If Ax = 0.2 at x = 1, Let y = approximation to estimate Ay use linear Ay =

A:

Q: The student should estimate the equation 0.24 0.24 + tan [0.247 + 2(0.27)n] π 1 1 =-+-tan(Tx + 2ny)…

A: Given function: gx,y=xπ+xπtanπx+2πy Point: 14, 14 To estimate: 0.24π+0.24πtan0.24π+20.27π Formulas…

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: Solve the following problems completely. Estimate (1.02) V0.99 using a local linear approximation of…

A:

Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

A:

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: Find the linear approximation of f(x) = In r at a = 1 and use it to estimate In(1.14). L(2) = %3D…

A: Please refer the attached image for complete solution.

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

A:

Q: 2. Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate…

A: The objective is to find the linear approximation to hx=x4  at  x=2 Use the linear approximation to…

Q: Let y = 5x + 3x + 4. If Ax = 0.1 at x = 5, use linear approximation to estimate Ay Ay =

A:

Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

A:

Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: 4x + 2x + 3. If Ax 0.1 at x = 5, use Let y = linear approximation to estimate Ay Ay 2

A: A detailed solution is given below

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the…

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

A:

Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

A:

Q: 2. Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate…

A: Linear approximation of a function f(x) at x = a is, fx=fa+x-af'a

Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

A:

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

A:

Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

A:

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

A:

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

A:

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given function is, h(x)=x4.

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…