Question
For small values of h, the function (16+h)^1/4 is best approximately by which of the following?
a. 4+h/32
b. 2+h/32
c. h/32
d. 4-h/32
e. 2-h/32
a. 4+h/32
b. 2+h/32
c. h/32
d. 4-h/32
e. 2-h/32
Answers
Steve
Even without doing much figuring, you know that it is near 2. That reduces your choices to B and E.
Since you have 16+h, it will naturally be B.
Now, the binomial theorem says that (16+h)^1/4 = 16^1/4 + 1/4 * 16^-3/4 * h + ...
= 2 + 1/4 * 1/8 * h
= 2 + h/32
Since you have 16+h, it will naturally be B.
Now, the binomial theorem says that (16+h)^1/4 = 16^1/4 + 1/4 * 16^-3/4 * h + ...
= 2 + 1/4 * 1/8 * h
= 2 + h/32