Guess the value of the limit (if it exists)

Question

Guess the value of the limit (if it exists) by evaluating the function at the given numbers.

Guess the value of the limit (correct to six decimal places), if it exists. (If an answer does not exist, enter DNE.)

Answer 1

someone hopefully has explained to you

the definition of derivative of f(x) at x₀ is f'(x₀)= lim h->0 of [f(x₀+h)-f(x₀)]/h

f(x)=x³ and x₀=4 fit the problem

since f'(x)=3x² for f(x)=x³

the limit for h->0 [(4+h)³-64]/h

is 3(4²)=48

Answer 2

The calculations for ±0.5.

Follow this model for the remaining values.