Lesson: L’Hôpital's Rule

In this lesson, we will learn how to apply L’Hôpital's rule to evaluate the limits of the indeterminate forms 0/0 and ∞/∞.

Worksheet: L’Hôpital's Rule • 25 Questions

Q1:

Find l i m 𝑥 0 𝑥 1 9 1 𝑥 + 2 5 5 .

Q2:

Determine l i m l n 𝑥 2 ( 𝑥 1 ) 𝑥 2 .

Q3:

Determine l i m 𝑥 0 1 9 𝑥 1 0 𝑥 5 𝑒 5 𝑒 𝑥 .

Q4:

Find l i m 𝑥 4 𝑥 3 𝜋 2 𝜋 8 8 𝑒 8 1 2 𝑥 + c o s .

Q5:

Find l i m 𝑥 0 5 𝑥 8 𝑥 7 𝑒 7 𝑒 + 1 .

Q6:

Determine l i m t a n 𝑥 0 2 𝑥 𝑒 1 2 𝑥 t a n .

Q7:

Find l i m 𝑥 2 𝑥 𝑥 9 8 1 7 4 9 .

Q8:

Find l i m 0 4 4 ( 𝑥 + 4 ) 𝑥 3 .

Q9:

Determine l i m 𝑥 0 2 𝑥 2 𝑥 1 7 1 3 1 .

Q10:

Find l i m ( 1 + 𝑥 ) 1 ( 1 + 5 𝑥 ) 1 .

Q11:

Find l i m 𝑥 0 1 3 1 3 4 4 ( 1 + 𝑥 ) ( 1 𝑥 ) ( 1 + 𝑥 ) ( 1 𝑥 ) .

Q12:

Suppose What can be said of the continuity of 𝑓 at 𝑥 = 𝜋 ?

Q13:

Find l i m 𝑥 2 𝑓 ( 𝑥 ) , where

Q14:

Given that l i m 𝑥 1 2 𝑥 ( 𝑚 1 ) 𝑥 𝑚 𝑥 + 1 = 3 , determine the value of 𝑚 .

Q15:

Determine l i m s i n 𝑥 0 𝑥 6 5 𝑥 2 1 .

Q16:

Determine l i m 𝑥 0 6 + 𝑥 2 6 4 4 𝑥 .

Q17:

Determine l i m s i n 𝑥 0 𝑥 2 𝑒 3 𝑥 2 2 𝑥 .

Q18:

Find l i m l o g 𝑥 0 𝑥 1 2 ( 2 𝑥 + 1 ) 1 0 1 .

Q19:

Determine l i m 𝑥 3 𝑥 3 8 𝑒 8 𝑒 9 𝑥 2 7 .

Q20:

Determine l i m s i n 𝑥 0 3 𝑥 3 𝑥 1 0 𝑒 1 0 𝑒 3 𝑥 3 𝑥 s i n .

Q21:

Given functions 𝑓 and 𝐹 , that are positive for large values of 𝑥 , we say that 𝐹 dominates 𝑓 as 𝑥 if

Use l’Hôpital's Rule to decide which is dominant as 𝑥 : l n 𝑥 or 𝑥 .

Q22:

Determine l i m 𝑥 2 𝑥 2 𝑥 2 𝑥 2 𝑥 5 𝑒 3 𝑒 3 𝑒 4 𝑒 .

Q23:

Find l i m 𝑥 3 𝑥 3 𝑥 2 𝑒 5 3 𝑒 1 .

Q24:

Determine

Q25:

Determine l i m l n 𝑥 0 2 2 3 7 𝑥 + 1 7 𝑥 .

Preview

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.