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9. Let f(x) = 2Vx. a) Find the differential of the function. b) Find the linearization...
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)
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).
Let f be the function defined as follows. y=f(x)=8x2-2x+10 (a) Find the differential of f. dy = (b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two decimal places.) dy = (c) Find the actual change in y if x changes from 2 to 1.97 and compare your result with that obtained in part (b). (Round your answer to two decimal places.) Δy =
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);
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?
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...
7. (a) (1 point) Define the linearization L(c) of a function f at a point a; (b) (1 point) draw a picture which gives a geometrical intepretation of the linearization; (©) (4 points) determine the linearization (1) of the function f(x) = fx 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);
Find the linearization of the function f(x) = 5 + x2 at x = 2. Explain how you arrive at your answer.
(1 point) Find the linearization of the function f(x,y) = 72 - 4x² – 2y at the point (3, 4). L(x,y) Use the linear approximation to estimate the value of f(2.9, 4.1) f(2.9, 4.1)