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Functions

# Limits of fuctions as x approaches a constant

When a function f is defined by some expression on some reduced neighborhood of a real number a, if we substitute a into this expression and it makes sense, then the outcome is the limit of f at a.

Look at the sample:

$\lim_{x\rightarrow3}\;\frac{5x^2-8x-13}{x^2-5}=\frac{5(3)^2-8(3)-13}{(3)^2-5}=\frac{8}{4}=2$

But, as you compute limits of functions as x approaches a constant, you can find several possible solutions:

• The limit is equal to a constant
• The limit is plus or minus infinity
• The limit does not exit
Try to compute the following limits:
Compute:
$\lim_{x\rightarrow-5}\;\frac{x^3-3x^2-25x+75}{x^2-25}$

 Solution: