If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real.

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

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

Determine the domain of the function : \( f(x)=\ln (x+2)+1 \) A. \( (-\infty, \infty) \) B. \( (-2, \infty) \) C. \( [2, \infty) \) D. \( (-\infty,-2) \cup(2, \infty) \)

I. Work Out (Show the necessary steps) For the rational functions (a-d) given below answer question (i-vi) each of the following i. Find the domain ii. \( \quad \) Find hole, if any iii. Find the vertical asymptote(s), if any iv. Find the horizontal or oblique asymptote, if any v. Find the \( x \)-intercept(s) and \( y \) - intercept(s) vi. \( \quad \) Prepare sign chart vii. Sketch the graph of each rational function a. \( \quad f(x)=\frac{x+2}{x^{2}-9} \)

(d) \( \sqrt{1+x^{2}} \)