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Please help!!! With limits math!?

0 votes
1) lim[x→8] (x2 − 5)/(x − 8) = ?
2) lim[x→−9] (x2 + 4)/(x + 9) = ?
asked May 4, 2013 in CALCULUS by andrew Scholar

3 Answers

0 votes

1)

italic lim with x rightwards arrow 8 below fraction numerator open parentheses x to the power of 2 minus 5 close parentheses over denominator x minus 8 end fraction equal fraction numerator open parentheses 8 to the power of 2 minus 5 close parentheses over denominator 8 minus 8 end fraction       (Substitute x = 8 in the limit function)

space space space space space space space space space space space space space space space space space space space space space equal fraction numerator open parentheses 64 minus 5 close parentheses over denominator 8 minus 8 end fraction        ( Simplify)

space space space space space space space space space space space space space space space space space space space space space equal fraction numerator open parentheses 59 close parentheses over denominator 0 end fraction              ( Denominator = 0, undefined)

space space space space space space space space space space space space space space space space space space space space space equal infinity

 

answered May 4, 2013 by diane Scholar
0 votes

2)

italic lim with x rightwards arrow minus 9 below fraction numerator open parentheses x to the power of 2 plus 4 close parentheses over denominator x plus 9 end fraction equal fraction numerator open parentheses open parentheses minus 9 close parentheses to the power of 2 plus 4 close parentheses over denominator minus 9 plus 9 end fraction                (Substitute x = -9 in the limit function)

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equal fraction numerator open parentheses 81 plus 4 close parentheses over denominator minus 9 plus 9 end fraction                         ( Simplify)

space space space space space space space space space space space space space space space space space space space space space space space space equal fraction numerator open parentheses 85 close parentheses over denominator 0 end fraction                            ( Denominator = 0, undefined)

space space space space space space space space space space space space space space space space space space space space space space space equal infinity.

 

answered May 4, 2013 by diane Scholar
0 votes

1)

From the L' hospital rule image

image

image

Evaluting this at x = 8

image

image

2)

From the L' hospital rule image

image

Evaluting this at x = - 9

image

answered Jul 15, 2014 by david Expert

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