Basic Calculus Quiz

1. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→1−
𝑥3 − 1 ?

2. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→1+
𝑥3 − 1 ?

3. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→1
𝑥3 − 1 ?

4. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→4−
𝑓 𝑥 ? 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→4+
𝑓 𝑥 ?

5. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→4
𝑓 𝑥 ?

6. 𝐶𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑜𝑓
𝑦 = 𝑥 + 2
𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→0
𝑥 + 2

7. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→1
𝑓(𝑥)
𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→−1
𝑓(𝑥)

8. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→3
𝑓(𝑥)
𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→5
𝑓(𝑥)

10. lim
𝑥→𝑐
𝑓 𝑐 = 𝑓(𝑐)
lim
𝑥→𝑐
𝑓 𝑐 ≠ 𝑓(𝑐)

11. lim
𝑥→1
−4 ∙ 𝑔(𝑥)
lim
𝑥→1
𝑓 𝑥
𝑔 𝑥

14. 𝐷𝑁𝐸
-∞
∞

15. Considering the graph below
𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→
𝜋
2
cos 𝑥?

16. Considering the graph below
𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→𝜋
cos 𝑥?

17. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→0−
cos (𝑥 +
𝜋
2
)?

18. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→0+
cos (𝑥 +
𝜋
2
)?

19. 𝑊ℎ𝑎𝑡 𝑖𝑠 lim
𝑥→0
cos (𝑥 +
𝜋
2
)?

20. 𝑒
1
𝑒

21. 𝑈𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑏𝑒𝑙𝑜𝑤, 𝑤ℎ𝑎𝑡 𝑖𝑠

23. {𝑥ǀ𝑥 ∈ ℝ}
{𝑥ǀ𝑥 ≠ 1}
{𝑥ǀ𝑥 ∈ ℝ, 𝑥 ≠ 0}
{𝑥ǀ𝑥 ∈ ℝ, 𝑥 ≠ 1}
The square root function 𝑓(𝑥) = 𝑥 is continuous on
[0, ∞).
Determine if the following functions are continuous on the
interval I.
≥