For each value of h, evaluate the following function. Round your answer to four decimal places. lim h->0 (4+h)^(3)-64/h
A) h=0.01
B) h=0.001
C) h=0.0001
D) h=-0.01
E) h=-0.001
F) h=-0.0001
For A I got 48.9
For B I got 48.99
For C I got 48.999
For D I got 47.9
For E I got 47.99
For F I got 47.999
Are these Right any help owuld be greatly appreciated
I've seen this one before and queried it before. As h tends to zero, (4+h)^3 approaches 64, but 64/h tends to either plus or minus infinity depending on which side h is approaching zero from, so this isn't what you're calculating. Could you check the function please?
I believe you meant to type
lim h->0 [(4+h)^(3)-64]/h since your calculation answer reflect that calculation.
BTW, my calculator got
A) 48.1201
B) 48.012
C) 48.0012
D) 47.8801
E) 47.9880
F) 47.99988
(I recognized your limit as the derivative of f(x) = x^3 as x approaches 4
eg.
f(x) = x^3
f'(x) = 3x^2
f'(4) = 3(4^2) = 48)
To evaluate the given function for each value of h and round the answer to four decimal places, we need to substitute the values of h into the expression and simplify the resulting expression.
The given function is:
lim h->0 (4+h)^3 - 64/h
To evaluate for each value of h, substitute the given values one by one into the expression and simplify:
A) h = 0.01
Substitute h = 0.01 into the expression:
(4 + 0.01)^3 - 64/0.01
Simplifying:
(4.01)^3 - 6400
Using a calculator, we find:
(4.01)^3 = 64.240601
64.240601 - 6400 = -6335.759399
Rounded to four decimal places, we get: -6335.7594
B) h = 0.001
Substitute h = 0.001 into the expression:
(4 + 0.001)^3 - 64/0.001
Simplifying:
(4.001)^3 - 64000
Using a calculator, we find:
(4.001)^3 = 64.032096
64.032096 - 6400 = -6335.967904
Rounded to four decimal places, we get: -6335.9679
C) h = 0.0001
Substitute h = 0.0001 into the expression:
(4 + 0.0001)^3 - 64/0.0001
Simplifying:
(4.0001)^3 - 640000
Using a calculator, we find:
(4.0001)^3 = 64.0040006
64.0040006 - 6400 = -6335.9959994
Rounded to four decimal places, we get: -6335.9960
Repeat the same steps for the remaining values of h, D, E, and F, that is substituting each value into the given expression, simplifying, and rounding to four decimal places.
D) h = -0.01
E) h = -0.001
F) h = -0.0001
Compare your calculated results with the given options to verify if they match.