Calculus 1 -Continuity Problem--Please help!?

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Calculus 1 -Continuity Problem--Please help!?

Let f(x) = (6/(x-7))-(84/((x^2)-49))

Calculate lim f(x) as x-->7 by first finding a continuous function which is equal to f everywhere except x =7.

lim f(x) as ->7 = _____

Thank you in advance!

2007-09-12 13:45:51 · 2 answers · asked by MA35 3 in Science & Mathematics ➔ Mathematics

2 answers

f(x) = 6/(x - 7) - 84/(x² - 49)

= 6(x + 7)/[(x - 7)(x + 7)] - 84/[(x - 7)(x + 7)]

= (6x + 42 - 84) / [(x - 7)(x + 7)]

= (6x - 42) / [(x - 7)(x + 7)]

= 6(x - 7) / [(x - 7)(x + 7)]

= 6 / (x + 7)

Lim x→7 {6 / (x + 7)} = 6/(7 + 7) = 6/14 = 3/7

2007-09-12 14:09:48 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋

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2007-09-16 09:07:35 · answer #2 · answered by Anonymous · 0⤊ 0⤋