Find the limits in Exercises 1–6.
3. lim(x→0⁺) (cox(√x))^(1/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

Find the areas between the curves y=2(log_2(x))/x and y=2(log_4(x))/x and the x-axis from x=1 to x=e. What is the ratio of the larger area to the smaller?

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)

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

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

e. arctan x = O(1)