Lim 4x2-100/x2-6x+5 X-5

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вопрос

To find the limit of the expression (4x^2 - 100) / (x^2 - 6x + 5) as x approaches 5, we can first simplify the expression by factoring the numerator and denominator:

(4x^2 - 100) = 4(x^2 - 25) = 4(x - 5)(x + 5
(x^2 - 6x + 5) = (x - 5)(x - 1)

Therefore, the expression simplifies to:

4(x - 5)(x + 5) / (x - 5)(x - 1)

Now, we can cancel out the common factor of (x - 5) in the numerator and denominator:

4(x + 5) / (x - 1)

Now we can substitute x = 5 into the simplified expression:

4(5 + 5) / (5 - 1) = 4(10) / 4 = 40 / 4 = 10

So, the limit of the expression (4x^2 - 100) / (x^2 - 6x + 5) as x approaches 5 is 10.