Linearization of a function
at
is defined by
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Here
At
Linearization is given by
Therefore
To find value of
substitute
That is
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Find the linearization of f(x)=1/x^2 at x=2 and use it to approximate the value of 1/1.98^2
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
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).
est f(x) = 3x? -) Find the linearization L(x) off at a = 4. ) Use the linearization to approximate 3(4.1)? c) Find 3(4.1) using a calculator d) What is the difference between the approximation and the actual value of 3(4.1)? a) The linear approximation is L(x)= b) Using the linearization, 3(4.1)2 is approximately (Type an integer or a decimal.) c) Using a calculator, 3(4.1) is (Type an integer or a decimal.) d) The difference between the approximation and the...
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.
7. (a) (1 point) Define the linearization L(x) of a function f at a point a; (b) (1 point) draw a picture which gives a geometrical intepretation of the linearization; (c) (4 points) determine the linearization L(x) of the function f(x) = Ýr at a = 27; (d) (4 points) use (c) to approximate the value 726.5 (express your answer as a rational number (a quotient); do not try to "simplify" it);
7. (a) (1 point) Define the linearization L(x) of a function f at a point a; (b) (1 point) draw a picture which gives a geometrical intepretation of the linearization; (c) (4 points) determine the linearization L(x) of the function f(x) = Ýr at a = 27; (d) (4 points) use (c) to approximate the value 726.5 (express your answer as a rational number (a quotient); do not try to "simplify" it);
9. Find the linearization L(x) of the function f(x) = Vx+5 at x = 4. Then, use L(x) to approximate V10. Round your answer to 3 decimal places. (10 points)
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
Find the local linearization of f (x) = ' near x = 1. f (x) ~ QG
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?