4) \( \lim _{x \rightarrow 0} \frac{1-\cos 2 x}{3 x} \) a) \( \frac{1}{3} \)

(8) \( \ln \sqrt{60}-\ln \sqrt{20}-\ln \sqrt{2} \)

\( \int \frac { e ^ { - x } } { 1 + e ^ { x } } d x \)

dériver: \( (3-x) e^{x}+1 \)

Let \( f \) be a strictly monotonic differen- tiable function on the closed interval \( [5,10] \) such that \( f(5)=6 \) and \( f(10)= \) 26. Which of the following must be true for the function \( f \) on the interval [5,10]? I. The average rate of change of \( f \) is 4. II. The absolute maximum value of \( f \) is 26 . III. \( f(8)>0 \). (A) I only (B) II only (C) III only (D) I and II (E) I. II. and III

(x) \( \frac{y}{x} \frac{d y}{d x}=\frac{e^{x}}{\ln y} \)