7. What integrals lead to logarithms? Give examples. What are the integrals of tan x, cot x, sec x, and csc x?

17. Even-odd decompositions

b. If f(x) = f_E(x) + f_O(x) is the sum of an even function f_E(x) and an odd function f_O(x), then show that

f_E(x) = (f(x)+f(-x))/2 and f_O(x) = (f(x)-f(-x))/2

112. True, or false? Give reasons for your answers.

a. 1/x⁴ = O(1/x² + 1/x⁴)

Find the limits in Exercises 1–6.

3. lim(x→0⁺) (cox(√x))^(1/x)

In Exercises 9 and 10, use implicit differentiation to find dy/dx.

9. y^e^x = x^y + 1

112. True, or false? Give reasons for your answers.

c. ln x = o(x+1)

111. True, or false? Give reasons for your answers.

e. arctan x = O(1)