Find g(e, 1) when g(x, y) = ln ⁡ ( x y + y − 1 )

Q: Choose True if the statement is correct, otherwise False. If an integration process produces a…

A: If an integration process produces a constant number, it cannot be added with the constant of…

Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: 1. Given: x3+y3=6xy To find y'by using implicit differentiation the implicit differentiation is…

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: An integrating factor for the differential dy + my = e-m² is dx equation

A: Given differential equation is dydx + my = e-mx

Q: 1. Differentiate the implicit equation with respect to x. x³ + y³ ln(x) + e²y = 4

A:

Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

A:

Q: Find the general solution using reduction of order. 1. y''=ln(x)

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: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

A:

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

Q: Solve the differential equati on. dz (log x) = –(log z) dx X

A:

Q: 2. (a). Use linear approximation to estimate ln 1.03. (b). Compute the percent error in your…

A:

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

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

A:

Q: When I am solving an integration question, how should I know which expression to equate to 'u' in…

A:

Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

A:

Q: A certain population is known to be growing at a rate given by the logistic equation = x(b – ax).…

A: Firstly find critical points. After that find second derivative , If second derivative less than…

Q: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: The integrating factor of the linear differential equation – (tanx)y = x is_ - O sinx O log(cosa)…

A: Given dydx-tanxy=x

Q: Solve ∫xn ln x dx in tegration by Parts?

A: Given:               ∫xn ln x dx Apply integration By Parts:              ∫xn ln x dx=ln x∫xn…

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: find fsubxz if (x, y, z) = ye^x + x ln z

A:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 4.3√√√7

A:

Q: Estimate the ln (1,1) and sec (0,1) using a linear approximation and without using any kind of…

A: Explanation we have to estimate ln(1.1) and sec(0.1) using a linear approximation method  linear…

Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

A:

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: Find 2 at the point (4,1,6) for -6x² + 7 ln xz + 4yz² – 2e? = 0 %3D

A:

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: How is ln x affected if x is multiplied by et?

A:

Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: According to the Ideal Gas Law, the pressure P, temperature T, and volume V of a confined gas are…

A: We have to use differentials to approximate the percentage change in pressure if the temperature of…

Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

A:

Q: Solue this Logistic stochostic differentialegh where ajb,c constant wit) ;win er Process by using…

A:

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

A:

Q: 5. Find by implicit differentiation for x + y = xy. dx

A:

Q: The approximation of the root x* of the function f(x) = ln(x + 1) - x + 3 accurate to within 10-2…

A: Introduction: Another recursive technique for approximating the polynomials' roots is the secant…

Q: What is the integrating factor of y' - 2xy x?

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.