Use l’Hôpital’s rule to find the limits in Exercises 7–52.
35. lim (x → 0⁺) ln(x² + 2x) / ln x

5. e^(2t)-3e^t = 0

Evaluate the integrals in Exercises 97–110.

103. ∫₁⁴ (ln 2 · log₂x / x) dx

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

79. y = θ sin(log₇ θ)

132. What is special about the functions

f(x) = arcsin((1/√(x²+1)) and g(x)=arctan(1/x)?

Explain.

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

27. y = θ(sin(lnθ) + cos(lnθ))

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

23. y = (x²+1)sech(ln x)

(Hint: Before differentiating, express in terms of exponentials and simplify.)