MATHEMATICS 120 PROBLEM SET 7
Due October 30, 2002
For full credit, please show all work.
1. (5 marks) Find all values of a for which the equation ln x = ax2 has exactly one solution.
2. (5 marks) A radioactive substance decays at a rate proportional to the amount present.
If 10% of the substance decays in 2 years, how long will it take for 80% of it to decay?
x
3. (5 marks) Show that arctan x = arcsin √
for all x.
1 + x2
4. (5 marks) Prove that cosh x > 1 +
x2
for all x 6= 0.
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Please read Sections 3.3–3.6 of the textbook (you may skip “interest on investments” and
”logistic growth”, Section 3.4). The recommended practice problems are: Section 3.3, 1–50
and 57–68; Section 3.4, 9–15; Section 3.5, 1–34 and 45–48; Section 3.6, 1,2,5,7.
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