Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) = In(1.18) =

Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

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

A: Use fundamental  theorem of calculus

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

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: The integration of dx is 4+x²

A: The given integral ∫dx4+x2 can be evaluated as, ∫dx4+x2=∫dxx2+22                =12tan-1x2+C…

Q: Find the total differential dz ZzxeX+y

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

A:

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

A:

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

A:

Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

A: To determine the tangent lines to the curve using derivatives

Q: Find the average rate of change of the function over the given interval. y =V4x + 1; between x 2 and…

A: To find the average rate of change of function y=4x+1 between x=2 and x=12

Q: Find the derivative of the given function. 5x y= In 6+x dy dx

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: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

A:

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

A:

Q: Use a linear approximation (or differentials) to estimate the given number. (8.09)2/3

A:

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

A:

Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

A:

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: Find the differential of the function. u = 2x +

A:

Q: For what function P is the integrating factor α(x) equal to ex?

A: Here the given integrating factor

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Let y = In(x'e2x ). Find dy/dx.

A:

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

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: Find the derivative. cos X d 78° dt dx 1 a. by evaluating the integral and differentiating the…

A:

Q: Find the average rate of change of the function over the given interval. y = V4x + 1; between x =0…

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 the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

A:

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

A:

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

A:

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

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

A:

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

A:

Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

A:

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

A:

Q: Confirm the approximations by using the linear approximation at x = 0

A: