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

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==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:
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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

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
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All AHSME Problems and Solutions

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