Barrueta Unit 2

Practice: Mixed Unit 1 & 2

1. (1D) lim!→!!

  !!!!!!!!!!!

2. (1E) lim!→!!

  !!!!!

!!!!

3. (1E) lim!→!

!"#!!!!"#!!

 

4. (1E) lim!→!"

  !!!! !!!!"

 

5. (1B, 1E, 1I)

lim!→!

 !"# !

!!! !!"#   !!!

 

6. (1F/G) lim!→!

  !!!!!"!"!!!!"!!!

 

7. (1H) Is the function

𝑓 𝑥 =𝑥 + 7                        𝑥 < 29                                      𝑥 = 23𝑥 + 3                    𝑥 > 2

continuous at x=2?

Barrueta Unit 2

8. (1I) lim!→!

  !"#!!  

9. (2B) Find the equation of the tangent line to 𝑦 = 3𝑥 sin 𝑥 at the x-value x=0

10. (2C) 2𝑥 cos 𝑥 sin 𝑥 ′

11. (2C) If 𝑦 = !"#$!!!!

, what is !"!"

12. (2D) Find 𝑓!!

!! if 𝑓 𝑥 = sec 𝑥

13. (2D) Find the points on the curve 𝑦 = !"#!

!!!"#! at which the tangent

is horizontal.

14. (2E) Differentiate: 𝑦 =𝑥  𝑠𝑖𝑛  !(5𝑥 + 1)