Limits at Infinity and L'Hopital's Rule

Question 1

What is lim x–>∞ f(x) ?

Answer 1

The y-value f(x) approaches as x goes to infinity

Question 2

What is lim x–> ∞ (e^x)?

Answer 2

+∞ because as x gets bigger and bigger, so does e^x

Question 3

What is lim x–>∞ (sin x)?

Answer 3

DNE because sin(x) does not approach a single y-value as x gets bigger. It just continues going up and down

Question 4

Which expressions are in indeterminate form?

Answer 4

0/0, ∞/∞, ∞ - ∞, 1^∞

Question 5

What does L’Hopital’s Rule say?

Answer 5

If f(x) and g(x) are continuous and f(x)/g(x) yields 0/0 or ±∞/∞, then
lim x–>a [f(x)/g(x)] = lim x–>a [f’(x)/g’(x)]

Question 6

What should you try before using L’Hopital’s Rule?

Answer 6

Using limit laws