Couple of AP Calculus Limits questions!

Test Preparation AP Mathematics & Computer Science
1

<p>I had a couple of questions over limits in calculus.</p>

<p>Directions: Find limit; if limit doesn't exist write DNE and explain why.</p>

<p>1) lim 1/x-1
x-->1^- (raised to negative means as it approaches the left) [I got approaches infinite but its wrong]</p>

<p>Directions: Discuss the continuity of each function. Classify any discontinuities as either removable or non removable</p>

<p>2) f(x) = absolutevalue(x+9)/(x+9) [I got does not exist; also wrong... would it be x- ]</p>

<p>Thanks!</p>

2

<p>1) negative infinity
2) x=-9, nonremovable</p>

<p>In number 1, the denominator is slightly negative when you plug in x=1-, so 1/0- is negative infinity. </p>

<p>In number 2, the function is undefined at x=-9 since the denominator is zero. The function is y=1 for x>-9 and y=-1 for x<-9, so the limit at x=-9 does not exist and as such the discontinuity is nonremovable.</p>