Question
Asked Jun 16, 2019
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Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)

lim x→10 
7x2 − 70x
x2 − 100
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Expert Answer

Step 1

The given function is f(x)=(7x2-70x)/(x2-100).

The limit is to be calculated.

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(7x2-70x (x2-100) lim x10

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Step 2

If we directly substitute x=10 than the fraction will be in the for 0/0 which does not exist. So in order to remove the discontinuity we will factorize the numerator and the denominator and then reduce it.

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(7x2- 70x) '(x-100)(x+10)(x-10) (a -b'=(a+b)(a-b)) lim l^(x-10) lim x10 7 lim 10 (x10

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Step 3

Since the discontinuity is being removed. ...

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7 7 lim 10(x10) 10+ 10 7 20

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Tagged in

Math

Calculus

Limits

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