MIDTERM EXAMINATION
CALCULUS II
A. Find the limit of the following:
1. lim (3𝑥 + 2)
𝑥→2
𝑥
2. lim (4 − )
2
𝑥→4
3. lim (𝑥 2 − 3)
𝑥→2
4. lim |𝑥 − 5|
𝑥→−5
5. lim (𝑥 2 + 3𝑥)
𝑥→−3
B. Use the rules of differentiation to find the derivative of the functions.
1. 𝑦 = 12
2. 𝑦 =
1
𝑥5
3. 𝑦 = 𝑥 16
4
4. 𝑔(𝑥) = √𝑥
5. 𝑓(𝑥) = 2𝑥 3 − 𝑥 2 + 3𝑥
6. ℎ(𝑥) =
2𝑥 2 −3𝑥−1
𝑥
3
5
7. 𝑓(𝑥) = √𝑥 + √𝑥
8. 𝑔(𝑡) = 𝑡 2 −
4
4
𝑡3
2
9. ℎ(𝑠) = 𝑠 5 − 𝑠 3
10. 𝑦 = 3𝑥(6𝑥 − 5𝑥 2 )
TOPICS
Groups
Topics
• Derivatives of the Sine and Cosine Functions
Group 1
• Derivatives Involving Sines and Cosines
• Rates of Change (include examples)
• Derivatives of trigonometric functions (include
Group 4
examples)
• Higher-order Derivatives (include examples)
Group 2
• Chain rule (include examples)
• General power rule (include examples)
• Simplifying Derivatives (include examples)
Group 3
• Trigonometric functions and the chain rule (include
examples)