L'Hôpital's Rule

The rule and its justification

Standard applications

The growth hierarchy proved

Other indeterminate forms

L'Hôpital's rule evaluates lim f/g for 0/0 by taking which expression?

What is lim x to 0 of (e^x - 1)/x, a 0/0 form, after one application of L'Hôpital's rule?

lim x to 0 of (1 - cos x)/x^2 requires two applications of L'Hôpital's rule. What is the final value?

The limit lim x to 0 from the right of x ln x is the indeterminate product 0 times infinity. Which rewriting puts it into a L'Hôpital form?

What does L'Hôpital's rule show about lim x to infinity of e^x over x^n for positive n?

For which of these limits is L'Hopital's rule NOT applicable, even though it may look tempting?

lim x to 0 of sin(3x)/x is 0/0. After one application of L'Hôpital's rule the limit becomes lim of 3 cos(3x) over 1. What number is this limit? Answer with a number.

lim x to infinity of (ln x)/x^2 is infinity/infinity. After one application the numerator becomes 1/x. What does the denominator become? Answer like 2x.

To evaluate lim x to infinity of e^x/x^3 by L'Hôpital's rule, the denominator must be differentiated until constant. How many applications are needed? Answer with a number.

lim x to 0 from the right of x ln x equals 0, so lim x to 0 from the right of x^x equals e to what power? Answer with a number.