find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

Q: evaluate the following integrals

A:

Q: Find the directional derivative of f at P in the direction of a. f(г, у, 2) — гу + 2?; P(5, —4, 3);…

A:

Q: solve the following ODE * y + xy = 6x/y

A:

Q: 2. Find the second degree Taylor polynomial of g(x) the value of –9.2. Express the estimated value…

A: The given function is: g(x)=1-3x3=(1-3x)13…

Q: Given: y = xcos (x); Find y". O y" = xsin (x) - 2 cos(x) %3D O y" = xsin (x) + 2 cos(x) O y" asin…

A: Formula:ddx(uv)=u dvdx+v dudxy = x cos(x)y' =x [-sin(x)] + cos(x)[1]y'= cos(x) - x…

Q: d dx

A:

Q: 3. -2 -5 Find the va lue of Hif Xi+xdx 3.

A: 3-2-518H-134=∫03x1+x2dxPut 1+x2=yas x →0 ,y→1as x →3 ,y→2differentiate on both…

Q: 1)" | Given: In(1 + x) if x < 1. n +1 n=0 1. Find the MMaclaurin series for f(a) = x In (1+ 5 )

A:

Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, P(4,…

A:

Q: Determine if the following statement is true or false. The lines L1 and L2 are skew. L:x = -1 + 21,…

A:

Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

Q: (y n?(1 + 3*) dy 1+ y? 2.

A:

Q: Let S be the surface given by the equation x^3+y^3-xz=5. What is the equation of the tangent plane…

A:

Q: 1 Use a limit comparison to test the convergence of |n+1 n=1

A: Given series ∑n=1∞1n+1 Recall limit comparison test

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Solution is here

Q: Ash buys 5 bunches of flowers. Each bunch contains 10 flowers. He gets 8 more flowers from his yard.…

A:

Q: x* + 3x? + 1) dx 5. 2e*dx 6. S(2e*+4*)dx 4.

A:

Q: A 1+ 2 + 3 + 4+ + 127 Σ > B, where .. n=1

A: First trace the rth  term then use the summation notation.

Q: 1 | zdnlzdz converges and I (In(x))" a positive number. Determine the values of p for which s of n…

A:

Q: Question 4 Find the derivative 4f (x)]; ƒ (x) = log, (sinh(arcsec 4-1) coth (arcsec ( 4-1)) 422-2…

A:

Q: Are the lines = 7+12t, y = 12–10r, z = 1+2t, and.x = 6+13t, y = 8+2t, z = 10–5t parallel? O No O Yes

A:

Q: Calculate -2 + lỉ. Give your answer in a + bi form. In polar form, use the angle 0 <0 < 2n. a - b -

A:

Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A:

Q: Consider e": for all æ E R. n! a. Determine the power series representation of f(x) = xe-5x² for all…

A: We have given the power series of ex  ex=∑n=0∞xnn!  for all x∈ℝ

Q: 39+ 5 dy (5y~7)2

A:

Q: Determine if the following functions are one-to-one by inspecting their graphs using the Vertical…

A: To determine if the following functions are one-to-one by inspecting their graphs using the Vertical…

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

A: Given :a) Oppositely directed to v=3,-12 and half the length of v.To find : w=(?, ?)b) Length 2 and…

Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

A:

Q: Solve triangle ABC if A = 24.7 degrees, C = 106.1 degrees and b = 34.0 cm   Show all work and…

A:

Q: 4. y = Vx, x = 0 , y = 2 , revolved at y axis %3D

A:

Q: Solve the following and show the complete solution. 2. Using Lagrange multipliers, find three…

A: Let x, y and z be the three positive number so,  sum of number   x+y+z=18

Q: Question 6 Differentiate: arcsin () + arccos (2) = 1 + arccos () = 1 %3D O y/x O (E) None of these O…

A: Derivative dydx of sin-1xy+cos-1yx=1

Q: Determine whether the lines Lj and L2 are parallel. L: x = 1– 2t, y = 4 + t, z = 6 – t L2: x = 4 –…

A: L1:x-1-2=y-41 =z-6-1=tdirection ratio: V1=(-2, 1, -1)L2:x-4-6=y+23 =z-7-3=tdirection ratio: V2=(-6,…

Q: n(n + 1)(2n + 1) 3. Le n be a positive integer. Use induction to prove || 6 j=1

A:

Q: 4. f (x) %3D (5х — 3)2 5. у %3D cos (5х) 6. f(z) — е5z?+72-13 7. у %3 4x2 + сot (3x) 8. f(x) —D (6х?…

A: Given problems:- 5.    y=cos(5x)  6.    f(z) = e5z^2+7z-13 7.   y=4x2+cot(3x)  To find:- Derivative…

Q: et +2e2t-et dt e2t +1 6.

A: Follow the procedure given below.

Q: Approximate the value of the given integral using the trapezoidal rule 12 y dx where the function y…

A:

Q: Let a = ci +j and b = 7i + 28j. Find c so that a and b are orthogonal. c =

A:

Q: 2x + 4 h(x) = 1 2x 1 f (x) = 1 –x g(x) = 3( x + 2x 6. | 3 -- 8. a.lim -4 · f (x) d.lim (8 · f(x) –…

A: Given:      fx=1-18x      gx=3x+2x6+4     hx=2x6-2x+13

Q: 2 x+1 dx J-1

A:

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: 2 f-2 xLo if where 14ーx2 if oLx 42 4 -x² if OL x -2

A:

Q: Barbara boards a Ferris wheel with a 50-foot radius. The center of the Ferris wheel is 60 feet above…

A: Given information:…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

A:

Q: 4x – 6 2. Let f(x) 1– (2x – 3)3 a. Find the Taylor series representation for f about x = 1.5 that is…

A: Let's find.

Q: Given the function f(x) = () a) Find a power series representation for f(z). п(п + 1) (n + 2):…

A: Let's find.

Q: 2х -1 dx 2 V3– x+x²

A:

Q: Question 1 Given y = Va - 2Vr 2; Find y'. 1-Vオ-2 %3D 2(-2) 7 O (E) None of the choices Va-2-1 Oy =…

A: