# 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 − 70xx2 − 100

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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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Step 1

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

The limit is to be calculated.

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.

Step 3

Since the discontinuity is being removed. ...

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