Question
Use differential, (i.e. linear approximation), to approximate cube root of 64.1 as follows:
Let f(x) = cube root of x. The linear approximation to f(x) at x = 64 can be written in the form y = mx+b. Compute m and b and find cube root of 64.2 via linear approximation
Let f(x) = cube root of x. The linear approximation to f(x) at x = 64 can be written in the form y = mx+b. Compute m and b and find cube root of 64.2 via linear approximation
Answers
dy = 1/3 x^-2/3 dx
At x=4, dy = 1/48 dx
So, use dx=0.2 to find dy, and add that to y(64)=4
Note also that since the slope is 1/48,
y-4 = 1/48 (x-64)
At x=4, dy = 1/48 dx
So, use dx=0.2 to find dy, and add that to y(64)=4
Note also that since the slope is 1/48,
y-4 = 1/48 (x-64)
Related Questions
Use differential, i.e., linear approximation, to approximate (125.4^(1/3)) as follows:
Let f(x)=x...
se differential, i.e., linear approximation, to approximate (8.4)^(1/3) as follows:
Let f(x)=(x )...
Use linear approximation, i.e. the tangent line, to approximate cube root of 27.05 as follows. Let f...
use tangent line approximation (linear approximation) to estimate The cube root of 1234 to 3 decimal...