Given #(sqrtx - 5) / (x - 25)# how do you find the limit as x approaches 25?

Answer 1

Evelyn Agard

#1/10#

#lim_(x to 25) (sqrt x - 5)/(x-25)#

#lim_(x to 25) (sqrt x - 5)/((sqrt x - 5)(sqrt x + 5))#

#lim_(x to 25) 1/(sqrt x + 5)#

#= 1/10#

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Answer 2

Paisley Johnson

To find the limit as x approaches 25 for the expression (sqrtx - 5) / (x - 25), we can simplify the expression by factoring the denominator. By factoring, we get (sqrtx - 5) / ((sqrtx - 5)(sqrtx + 5)). The (sqrtx - 5) terms cancel out, leaving us with 1 / (sqrtx + 5).

Now, we can substitute x = 25 into the simplified expression. Plugging in x = 25, we get 1 / (sqrt25 + 5), which simplifies to 1 / (5 + 5) = 1 / 10 = 0.1.

Therefore, the limit as x approaches 25 for the given expression is 0.1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.