Determine the following limits.
lim x→−5^+ x − 5 / x + 5...

Question

Determine the following limits.

lim x→−5^+ x − 5 / x + 5

Accepted Answer

Welcome back, everyone find the limit limit of X plus two divided by X minus three. When X approaches three from the left, there are four answer choices. A says infinity B negative infinity C zero and D three. So let's start this problem by attempting direct substitution. We have limit. When X approaches we from the left of X plus two divided by X minus three, applying direct substitution, we get three from the left plus two divided by three from the left minus three. Now, for the numerator, if we drop, we from the left, we simply get we plus T which is five. The reason why we drop it is because no matter from which side we approach three, we still get a limit of five. However, for the denominator, this is where it becomes important. If we're approaching three from the left and subtracting three, we get zero and we're approaching that zero from the left right now, three minus three is zero. And it is really important to understand that we are approaching zero from the left because approaching three from the left gives us the overall difference from the left. If we are approaching three from the right, then we're approaching zero from the right. So now the reason why this becomes so important is because we have a number divided by zero, which essentially always gives us a limit of infinity. But we're interested in the sign of infinity. We're dividing positive five by zero from the left. So basically an infinitely small negative number dividing a positive number by a negative number gives us a negative number. So the infinity we'll have a negative sign. Meaning the answer choice for this problem would be option B negative infinity. Thank you for watching.

Determine the following limits.
lim x→−5^+ x − 5 / x + 5

Key Concepts

Limits

One-Sided Limits

Rational Functions

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