Special wallpaper that costs $2 per square foot. How much will the wallpaper cost in total?
2 answers:
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Using the definition,
The numerator in the difference quotient is
Multiply the numerator and denominator by the conjugate of this expression,
The modified numerator reduces to a difference of squares,
Simplify this to get
Since x is approaching 4, it never actually takes on the value of 4, so (x - 4)/(x - 4) reduces to 1. Then the limit is equivalent to
and the remaining limand is continuous at x = 4, so that