Which of the following functions has an asymptote at \( y=5 \) ? A. \( f(x)=\ln (x+1)+5 \) B. \( f(x)=e^{-x}+5 \) C. \( f(x)=\sqrt{x}+5 \) D. \( f(x)=x^{2}+5 \)

Eveluate \( \frac{\ln \sqrt{60}-\ln \sqrt{20}-\ln \sqrt{2}}{\ln 9-\ln 1} \)

4. Найдите область определения функции \( y=1-\sqrt{3 t g \frac{x}{2}-\sqrt{3}} \).

The population of a certain species in a protected area can be modeled by the function \( P(t) = 200 + 50 \sin(t) \), where \( t \) is measured in years. Determine the total population increase over one complete cycle (from \( t=0 \) to \( t=2\pi \)).

Q. 41. Find all asymptotes of the curve \( x^{3}+y^{3}=3 a x y \). (Bhopal 1991, 2000; Sagar

10) If \( f(x)=\frac{1}{x-a}+b \), then \( f^{-1}(a)+f(b)= \)