Let f(x) = ln(1 + x²). Use a linearization to estimate In 2. Explain clearly what...
Consider the function f(x) = x ln(3x+1) (a) Find the derivative (b) Write the linearization of f at x = 2 (c) Use your linearization to estimate f(2.5) (d) Draw a sketch of the function in the space below, using a solid line for f(x). On the same coordinate plane, draw a sketch of the linearization using a dotted line. Please use values 0<x<5(or equal to) on the x-axis (e) Is your estimate from part c an overestimate or underestimate?
Suppose you intend to estimate ln(1.2) using a linearization ?(?) = ?(?) + ?′(?)(? − ?). a. What are appropriate choices for ?(?) and ?? b. Set up and evaluate the computation that would give you the desired estimate for ln(1.2).
Question 9 Let f(x,y) = y Væety. Find the linearization of f at (1, -1). Use the linearization to approximate f(0.9, -1.1).
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Find the linearization of the function f(x) = 5 + x2 at x = 2. Explain how you arrive at your answer.
Please answer all parts of the question and make writing legible f(x)-sin(x) a. Use differentials and linearization to estimate the value sin(1.02) b. Sketch the graph that demonstrates the concepts of linearization as it pertains to this problem given c. Based on the graph sketched not what is on the calculator, is your estimate an overestimate or underestimate? Explain the reasoning referring to the sketch in part b. Verify your conclusion by using the calculator to find the actual value...
Find the linearization of f(x)=1/x^2 at x=2 and use it to approximate the value of 1/1.98^2
4. (5 pts) For f(x) = 210 a. Find the linearization of f(I) at =1 b. Use your linearization to estimate (1.003) 10
Use the linearization of f(x) = x + 3 at 2 = 1 to approximate 3.98 Select one: V3.98 2.995 O 3.98 1.995 O None of these answers O V3.98 3.98 3.98 1.5 O page
9. Let f(x) = 2Vx. a) Find the differential of the function. b) Find the linearization of f(x) at a = 4. c) Use your answer in part (a) to approximate the value of 2/3.