1
The Natural Exponential Function- HW Problems
Solve for 𝑥.
1. 𝑒(2−3𝑥) − 4 = 0
2. ln(𝑥 − 1) − ln(𝑥 + 1) = 1
Evaluate the following limits.
𝑒2𝑥 +𝑒𝑥
3. lim
𝑥→∞ 𝑒3𝑥 +1
1
(2−𝑥)
4. lim 𝑒
𝑥→2+
Evaluate.
1 4
5. ln( )
𝑒
6. ln [𝑙𝑛 (𝑒(𝑒 ) )] 7. 𝑒 −3 ln(2)
Find the derivative.
8. 𝑦 = 𝑒tan(𝑥) + 𝑒−3𝑥
9. 𝑦 = ln(𝑒𝑥 + 1)
2
10. 𝑦 = 𝑒ln(𝑥 +1)
𝑒𝑥 +𝑒−𝑥
11. 𝑓 (𝑥 ) = tanh(𝑥 ) =
𝑒𝑥 −𝑒−𝑥
12. 𝑦 = 𝑡[sin(𝑒2𝑡 )]
The Natural Exponential Function- HW Problems
Solve for 𝑥.
1. 𝑒(2−3𝑥) − 4 = 0
2. ln(𝑥 − 1) − ln(𝑥 + 1) = 1
Evaluate the following limits.
𝑒2𝑥 +𝑒𝑥
3. lim
𝑥→∞ 𝑒3𝑥 +1
1
(2−𝑥)
4. lim 𝑒
𝑥→2+
Evaluate.
1 4
5. ln( )
𝑒
6. ln [𝑙𝑛 (𝑒(𝑒 ) )] 7. 𝑒 −3 ln(2)
Find the derivative.
8. 𝑦 = 𝑒tan(𝑥) + 𝑒−3𝑥
9. 𝑦 = ln(𝑒𝑥 + 1)
2
10. 𝑦 = 𝑒ln(𝑥 +1)
𝑒𝑥 +𝑒−𝑥
11. 𝑓 (𝑥 ) = tanh(𝑥 ) =
𝑒𝑥 −𝑒−𝑥
12. 𝑦 = 𝑡[sin(𝑒2𝑡 )]
