Question

lim x--->0 (2+3x)^3-8/x

Answer 1

Without any algebra or calculus, the form is indeterminate 0/0.
What does an indeterminate form suggest?

Answer 2

does not exist?

Answer 3

but the answer is 36

Answer 4

First, you're missing a parenthesis after the -8.
L'Hospital's rule is the correct direction.

Answer 5

im not super familiar with that rule yet. im substituting a number for zero?

Answer 6

If the limit is in an indeterminate form, you can use L'Hospital's rule. Take the derivative of the numerator and denominator and that is equal to your original limit.

\[\lim_{x \rightarrow 0} ((2+3x)^{3}-8) / x = \lim_{x \rightarrow 0} (81x ^{2}+108x+36) / 1\]

Answer 7

yeah we havent been taught that in Calc one yet.
neat trick though. i dont know how to find derivatives yet.