- Topic
- L’Hôpital’s rule
- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
L’Hôpital’s rule practice question 3
Evaluate the limit.
What do the top and the bottom each tend to as ? That form decides which tool you may use.
Both numerator and denominator are 0 at . Differentiate each: and .
A number, as a fraction or a decimal.
How sure are you?
Theory UBC Math 100 §6CLP-1 §3.7Key results
Worked solution
Strategy
A 0/0 form with an exponential and a sine: one application of the rule, with the chain rule supplying the constants 3 and 2.
Working
Form 0/0.
Differentiate top and bottom, then substitute.
Answer
The answer is three halves.
Check
At x = 0.001 the quotient is about 1.502, close to 3/2.
Where this goes wrong
Dropping the inner derivatives to get e3x/cos(2x) → 1. The 3 and the 2 from the chain rule are the whole answer.
Leans on
The chain rule, from The chain rule and logarithms
Try a similar question
Evaluate the limit.Saved in this browser only.