1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) / dx = dx = (b) 2x+1 (c) (e) / dx = x2 +1 3 In x dx = хе

Q: (1) x² + 3xy+y? = 4 (2) -=y² +1 x-y

A:

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b.…

A: This is a question related to differential equation. Based on the formula of integrating factor we…

Q: use appropriate substitution to solve differential equatio dy/dx-(2/x)y=-x^2y^3

A:

Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: Solve for the differential of y when y = sinæx, x=-, and dx=- 3 2 4 4 -iN

A:

Q: 1-dt 3- Ln(t) dt. Q10:- Calculate dx J2x t2

A: Use fundamental  theorem of calculus

Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

A:

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

A:

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

A:

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: 10. Find the derivative of y = ln 4**+1) In 4 dy A) dx 2x dy 2x In 4 B) dx dy 2xIn 4 C) dx 4(*+1) dy…

A:

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

A:

Q: Find dy/dx by implicit differentiation. y3+9xy+4x3-12x=0

A: Here we can find the derivative as below

Q: 7. Differentiate the following function.   y=ln(x+6)+ln5 dy/dx=nothing   Enter your answer in the…

A: Differentiate the following function.      y=ln(x+6)+ln5

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

A:

Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: 5. dx of y = (1+e-*)²/(1-e-*)

A: We need to find the derivative of the given function.

Q: (a) Evaluate xe* dx using substitution method. (b) Evaluate | 6xe* dx using integration by part…

A: We will find out the required value.

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: 4- cosh x2 dy + (sinh x)y = e-* dx

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: |e2* sin (3x) dx sinh (Vx) dx

A: We have to evaluate given integration.

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 4. Use implicit differentiation to find dy/dx. (a) ye" = x" + 1 In x (b) ymz = x"

A:

Q: 8) S(eax - e-ax) dx 9) S; sinh x dx 1+cosh x

A: Answer to question number 8 and 9 are as below,

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

A:

Q: dy Find by implicit differentiation. dx 14 In x= 18 - In y dy dx (Type an exact answer.)

A: Consider the given expression 14ln x=18-ln y.

Q: The Bernoulli's equation dy +ytanx = y'sec x after multiplying dx -2y and use appropriate…

A:

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Find dy/dx by implicit differentiation. x4/3 + y4/3 = 1

A: Given that: x4/3+y4/3=1

Q: بال 20 S 3y م + dx dy

A: The double quintessential is maximum typically used to calculate the floor vicinity of a…

Q: Let y = 5(square root x) Find the change in y. Delta-y when x = 5 and delta-x = 0.1 Find the…

A: The given function is y=5x. We need to find ∆y when x=5 and ∆x=0.1. Also, to find dy when x=5 and…

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

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Q: B4. Evaluate e* sin x dx by using integration by parts method.

A:

Q: (1) | cosx In (sin x) dx (2) [ xe -TX | хе dx x (3) x -16 dx

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…

Q: | (In x)2 dx Use integration by parts.

A: