Fall 2014
WIR8 (4.2 – 4.6)
Math 151
1. Given a one-on-one function 𝑓 𝑥 =
4𝑥+3
2𝑥+1
1
, find 𝑔′ (1)
2. Given a one-on-one function 𝑓 𝑥 = 𝑥 3 − 2𝑥 2 + 5𝑥, find 𝑔′ (10)
3. Given 𝑓 4 = 2, 𝑓 ′ 4 = −3, 𝑓 2 = 6, 𝑓 ′ 2 = −5, 𝑓 6 = 4 and 𝑓 ′ 6 = −1, if
𝑔 = 𝑓 −1 , find 𝑔′ (2).
4. Rewrite log 4 16 = 2 as an exponential equation.
5. Rewrite using log laws: log 𝑎
6. Solve for a: log 8 𝑎 =
𝑥2 𝑧
𝑦3
2
3
7. Calculate the following:
a. log 2 8
1
b. log 5
625
c. 3 log 2 + 2 log 3 − 4 log 5 + log 25
8. Solve for x: log 2 − 𝑥 + log 5 − 𝑥 = 1
1
9. Find the inverse of the function 𝑓 𝑥 = 5𝑒 𝑥
10. Find the limit for lim𝑥→∞ [ ln(𝑒 2𝑥 + 2𝑒 𝑥 ) – ln(2𝑒 2𝑥 + 𝑒 𝑥 )]
11. Find the derivatives for the following:
a. 𝑓 𝑥 = ln −3𝑥
b. 𝑓 𝑥 = ln(| sin 𝑥|)
c. 𝑓 𝑥 = log 5 (𝑥 2 + 4)
d. 𝑓 𝑥 = 𝑥 2 ln(3 + 2𝑥)
e. 𝑓 𝑥 =
𝑥 2 sin 𝑥
1+2𝑥
12. Find the derivative of 𝑓 𝑥 = 1 + cos 𝑥
13. Find the derivative for 𝑓 𝑥 =
1
𝑥
5
5𝑥+3 3 𝑒 5𝑥 +3
7𝑥 2 +2 2 sin 7 𝑥
14. Strontium 90 is a radioactive isotope with a half life of 25 years. If there are 20 mgs of
this isotope today, how much of it will be left after 15 years? After how many years will
there be only 2 mgs of Strontium 90 left?
15. A cup of coffee at a temperature of 900C is placed in a room which is at a temperature of
200C. If the cup of coffee cools to 750C after 5 minutes, at what temperature will it be
after 15 minutes? Use Newton’s law of cooling for this problem.