Difference between revisions of "1950 AHSME Problems/Problem 40"

m (Problem)
 
Line 1: Line 1:
 
==Problem==
 
==Problem==
  
The limit of <math> \frac {x^2\minus{}1}{x\minus{}1}</math> as <math>x</math> approaches <math>1</math> as a limit is:
+
The limit of <math> \frac {x^2-1}{x-1}</math> as <math>x</math> approaches <math>1</math> as a limit is:
  
 
<math>\textbf{(A)}\ 0 \qquad
 
<math>\textbf{(A)}\ 0 \qquad

Latest revision as of 22:56, 13 March 2015

Problem

The limit of $\frac {x^2-1}{x-1}$ as $x$ approaches $1$ as a limit is:

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ \text{Indeterminate} \qquad \textbf{(C)}\ x-1 \qquad \textbf{(D)}\ 2 \qquad \textbf{(E)}\ 1$

Solution

Limits do not take the value of the limiting function at the specified value into account, so we are essentially being asked to find the limit of $x+1$ as $x$ approaches $1$. This is simply $\boxed{\textbf{(D)}\ 2}$.

See Also

1950 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 39
Followed by
Problem 41
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS