Q1 (10 pts): For the function g(x) = x²-4 x²-2x (x+2)(x-2) x(x-2) = x+2 when x 2. χ 1) Using proper interval and set notation, give the domain of g(x). 2) Give the value of the y-intercept of g(x). If there are no y-intercepts, state NONE. 3) Give the value(s) of the x-intercepts) of g(x). If there are no x -intercepts, state NONE. 4) Give the equation(s) of the horizontal asymptote(s) of g(x). "y = #". 5) Give the equation(s) of the vertical asymptote(s) of g(x). "x = #". 6) Classify g(x) as either an even function, an odd function, or neither. Justify your choice by evaluating a pair of opposite x-values in the domain of g(x). 7) Find lim g(x) = x-0- lim g(x): x→0+ lim g(x) = x-2- lim g(x) = x+2+ 8) Using the "simplified" form g(x) = = x+2 χ , find g'(x). lim g(x) = x-0 lim g(x) = x→2 9) Find any intervals of increase for g(x). If there are no intervals of increase, state NONE. Continued Preview File Edit View Go Tools Window Help く AMAT 112_HW 08.pdf Page 2 of 3 ✓ PLC ୪ Q Search 10) Find any intervals of decrease for g(x). If there are no intervals of decrease, state NONE Q2 (10 pts): Use l'Hospital's Rule, fi appropriate, to find the following limits: lim x+7 sin x x-0 sin 4x 11) Find the location (x and y values) of all local max / local min. If there are no local extreme points, state NONE. 12) Using the "simplified" form g(x) = x+2, find g"(x). x 13) Find any intervals where g(x) is concave up. If there are no such intervals, state NONE. 14) Find any intervals where g(x) is concave down. If there are no such intervals, state NONE. 15) Find the location (x and y values) of all inflection points. If there are no inflection points, state NONE. Q2 on next page. lim x sin 80+x ( Thu Jul 25 9:41 PM