In Exercises 9 and 10, use implicit differentiation to find dy/dx.
9. y^e^x = x^y + 1

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 limits in Exercises 1–6.

3. lim(x→0⁺) (cox(√x))^(1/x)

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?

Find the limits in Exercises 1–6.

5. lim(n→∞) (1/(n+1) + 1/(n+2) + ... + 1/(2n))

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?