If y = Vln(x)+ In(/E), then y' Select one: 1 O a. (z)u1^z O b. (z)u1^z O c. 2z /In(z) Od. 2z /In(z) 2.z

Q: f (x, y, z) = ln(x2 + z) + y2 exz. Fin

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A: Given that Φ(x,y) = ex-y and Φ(ln2,ln2)=1. Now by using the technique of linear approximation we…

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Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: Find the most general antiderivative. 9 dx -x2 x zX - IN

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: Find the total differentials of w=2z2 ysinx

A: The detailed solution is given below Thank you

Q: If xy In(3 sinh( 3x)), then x2y'= %3D Select one: Ox coth( 3x ) - In( 3 sinh(3x)) 09x coth( 3x ) - 3…

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Q: 11. Verify that wxy = Wyx for w = e* + x ln y + y ln x

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Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

Q: Tind dʻz of z- In (xy) Find d²z z - In (xy)

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Q: Integrates PDE SE ニー Zく Z8 te

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Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: 1. Evaluate S(x + y)dxdy by reversing the order of integration.

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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Q: Find the total differential of  w=x3yz+xy+z+3

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Q: 23) Fnd yp of yll-ly'+hy=48+2tesin2t (Oo not evaluate cefficients)

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Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Find the total differential of z = In (2x – 3y).

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Q: Find the Integration of: Ja (3sint + esin t) cost dt In 3 2

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Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

Q: a) the linear approxinma ion to the function + 3X ät

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Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: Let y=3sqrt(x)Find the change in y, Δy when x=5 and Δx=0.2 Find the differential dy when x=5 and…

A: Given function is Change in y is calculated as follows. when x=5 and Δx=0.2

Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method