Written Assignment for Unit 7 with solutions
• L’Hopital’s Rule
• Newton’s Method
• The Integral
1. Calculate the indicated limit. lim
𝑥–>3
𝑥2+4𝑥−21
𝑥2−7𝑥+12 . If a limit does not exist then answer +∞, – ∞, or
DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it.
And whenever you apply L’Hopitals rule, indicate that you are using it.
Answer: –10
2. Calculate the indicated limit. lim
𝑥–>0
tan 3𝑥
ln(1+𝑥) . If a limit does not exist then answer +∞,– ∞, or
DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it.
And whenever you apply L’Hopitals rule, indicate that you are using it.
Answer: 3, used L’Hopitals rule
3. Calculate the indicated limit. lim
𝑥–>0
sin 𝑥−𝑥
𝑥2 . If a limit does not exist then answer +∞,– ∞, or
DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it.
And whenever you apply L’Hopitals rule, indicate that you are using it.
Answer: 0, used L’Hopitals rule
4. Calculate the indicated limit. lim
𝑥–>0
sin (6 𝑥)
sin (3 𝑥) . If a limit does not exist then answer +∞, – ∞, or
DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it.
And whenever you apply L’Hopitals rule, indicate that you are using it.
Answer: 2, used L’Hopitals rule
5. Which of the following are indeterminate forms? 0
0,0
∞,∞
0,∞
∞
Answer: 0
0,∞
∞
6. Use Newton’s Method to determine 𝑥1 and 𝑥2 for the function 𝑓(𝑥)= 𝑥 𝑐𝑜𝑠 (𝑥)− 𝑥2 and the
value of 𝑥0= 1.
Answer: 𝑥1= 0.8002329432 and 𝑥2= 0.7440943985
7. Use Newton’s Method to determine 𝑥1 and 𝑥2 for the function 𝑓(𝑥)= 𝑥3− 7𝑥2+ 8𝑥 − 3 and
the value of 𝑥0= 5.
