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AURORKA [14]
3 years ago
15

Find the following limit or state that it does not exist. ModifyingBelow lim With x right arrow minus 2 StartFraction 3 (2 x min

us 1 )squared minus 75 Over x plus 2 EndFraction
Mathematics
1 answer:
leva [86]3 years ago
6 0

Answer:

-60

Step-by-step explanation:

The objective is to state whether or not the following limit exists

                                \lim_{x \to -2}  \frac{3(2x-1)^2 - 75}{x+2}.

First, we simplify the expression in the numerator of the fraction.

3(2x-1)^2 -75 = 3(4x^2 - 4x +1) -75 = 12x^2 - 12x + 3 - 75 = 12x^2 - 12x -72

Now, we obtain

                         12(x^2-x-6) = 12(x+2)(x-3)

and the fraction is transformed into

                       \frac{3(2x-1)^2 - 75}{x+2} =  \frac{12(x+2)(x-3)}{x+2} = 12 (x-3)

Therefore, the following limit is

       \lim_{x \to -2}  \frac{3(2x-1)^2 - 75}{x+2} = \lim_{x \to -2}  12(x-3) = 12 \lim_{x \to -2} (x-3)

You can plug in -2 in the equation, hence

                        12 \lim_{x \to -2} (x-3) = 12 (-2-3) = -60

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