Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following represents L(x)?

Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

A:

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

A:

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

A:

Q: Find a formula for the error E(x) in the tangent line approximation for f(x)=√(1+x) near x=a=0 ?

A: Differentiate the function f with respect to x, to find f'(x). Substitute 0 for x in fx=1+x and…

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = x ln(x…

A:

Q: Find the equation of the tangent line to the function f(x) = e*-1 In(x + 1) when x = 0.

A:

Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

A:

Q: Consider the graph of the function f(x) = ln(1 + x²) for x > 0. 1. Find f'(x). 2. At which value of…

A: Ta which value of x the slope of tangent line the greatest.

Q: Find the equation of the tangent line and the normal line to the graph of the function b) f(x) = x…

A:

Q: Differentiate. f(x) = In ( In (8x)) f'(x) = Compute the following derivative using the method of…

A:

Q: Find the slope of the tangent line to x2y2+x sin(15y) = 4 at any point (x, y) on the curve.

A:

Q: Find the equation of the tangent line to f at x = a. f (x) = x2 + x, a = 1

A:

Q: Find the derivative of y with respect to x. y = 9 In (6 In x) dy %3D dx

A:

Q: f(x) = t cosh (t² – 1) dt 1+ln (x) tan-lt

A: From the Fundamental theorem of calculus, If…

Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: Find the exact equation (without decimal approximations) of the tangent line in the form y = mx + b…

A:

Q: Find the tangent line to the function y = x^2 at (1,1).

A: The given function is: y=x2 Now differentiate it with respect to x: y'=ddxx2y'=2x Put x=1 in y' to…

Q: Determine the value(s) of x such that f(x)=e*-6x have a horizontal tangent line. Answer in exact…

A: Given that  function f(x) = e3x - 6x and we determine the value of x the function have horizontal…

Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

A:

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: Find an equation of the tangent plane to z=ln(2x+3y) at the point (1, 1, ln5).

A:

Q: 2. Use implicit differentiation to find the tangent line to the given curve at the given point P (a)…

A:

Q: Consider the derivative function h (x) = -sec? (x) + 9. What is the general antiderivative of h?

A:

Q: The equation of the tangent line to f(x) = In x at x = 1 is O y = x - 1 O y = x O x = 1

A:

Q: Find the tangent line of f(x) = V1+x at a = 0 and use it to give an approximation for V1.01

A: To find the tangent line of the below function at a = 0. fx=1+x3

Q: Find the equation of the tangent line of e –z = 4x at z = 3.

A: Here we find equation of tangent at x=3

Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

A:

Q: Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х —…

A: To find the equation of tangent line to the curve at x=1

Q: 2. Use implicit differentiation to find the tangent line to the given curve at the given point P (a)…

A:

Q: find the derivative of y with respect to x, t, or u,as appropriate. y = e^(cos t + ln t)           .…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Determine the slope of the tangent line to the curve y= In x^2 at x = e^2

A: The given curve is

Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

A:

Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

A:

Q: Compute the derivative of h(sin x) at x = , assuming that h' (0.5) = 10.

A:

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

A:

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

A:

Q: The equation of the tangent line of f(x) 3 e* at x = 0 is %3D y

A: We have to find the equation of the tangent line of the given function at the given point   The…

Q: Find the equation of the tangent line of f (x)= x² In x at x=1.

A:

Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

A:

Q: Find the equation of the tangent line to the curve f(x)= Va. Assume f'( x) 1 at x = 4.

A:

Q: Compute the derivative of h(sin(x)) at x = T/6, assuming h'(0.5) = 10:

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = [(x −…

A: Consider the given function.

Q: Find a formula for the tangent line to f(x) = x² – x at x = 0

A:

Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value.   f(x) = x ln(x…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e-X…

A: Given: f(x)=e-xln(x)

Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: Find the equation of the tangent line to the graph of F(x) = c2x²+2x+1 sech a ev dy at x = 0.

A: