7. (a) (1 point) Define the linearization L(x) of a function f at a point a;...
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(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);
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)
Find the linearization L(x,y) of the function at each point. f(x.y) = x2 + y2 + 1 a. (3,3) b. (1,3) a. L(x,y)=
(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)
3 px (1 point) Given It find the linearization of F at a = L(x) =
Find the linearization L(x,y) of the function f(x,y)= e 3x cos (y) at the points (0,0) and RIN The linearization at (0,0) is L(x,y)= (Type an exact answer, using a as needed.) The linearization at 0. is L(x,y)= 0 (Type an exact answer, using a as needed.)
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?
Find the linearization L(x,y) of the function f(x,y)=X - 9xy +7 at Po(5.2). Then find an upper bound for the magnitude El of the error in the approximation fix.y) LIX.y) over the rectangle R X-5 30.5, ly-2 30.5. The linearization of fis Lix,y)=
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.