Asked by Henry
use tangent line approximation (linear approximation) to estimate The cube root of 1234 to 3 decimal places. Hint: the equation should be y=f'(x0)(x-x0)+f(x0)
11^3=1331 can be easily computed using binomial theorem.
I used linear approximation and got 10.733, but it is not correct to 3 decimal places. Cube root of 1234 is 10.726
11^3=1331 can be easily computed using binomial theorem.
I used linear approximation and got 10.733, but it is not correct to 3 decimal places. Cube root of 1234 is 10.726
Answers
Answered by
Steve
You are correct. It's just that at x=11, the linear approximation isn't very good when you get var away from 11.
You were not asked to get an approximation which agrees with the true value to 3 places, just to get a value out that far.
Extra credit: how far away from 11 can you go and still have the linear approximation good to three places?
You were not asked to get an approximation which agrees with the true value to 3 places, just to get a value out that far.
Extra credit: how far away from 11 can you go and still have the linear approximation good to three places?
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