Determine the following limits.
lim x→3^- x − ...

Question

Determine the following limits.

lim x→3^- x − 4 / x^2 − 3x

Accepted Answer

Welcome back everyone to another video solve for the limit limit of X minus T divided by X squared minus four X. When X approaches four from the right, we're given four answer choices. A says negative infinity, B says infinity C zero and D two. So let's begin this problem with the direct substitution. We get limit when X approaches four from the right. And we can essentially rewrite this function as X minus two. If I did buy, if we factor out X for the denominator, we get X multiplied by X minus four. Now using direct substitution, we get four from the right minus two divided by four from the right multiplied by four from the right minus four. Now let's simplify that in the numerator, we get four minus two, which is two. It doesn't matter if we approach four from the right or the left because the overall result is not zero, right. We just include two in the denominator four from the right as a factor simply becomes four, right? Because it is a positive number and then we have a difference four minus four, which is basically zero. And this is where it becomes important. If X approaches four from the right, then X minus four approaches zero from the right as well because X is slightly greater than four, right, we're approaching four from the right. So we get four multiplied by zero from the right overall, this simplifies his two divided by zero from the right because four multiplied by zero from the right is basically zero from the right. Whenever we are evaluating a limit of a function that gives us a form of a number divided by zero, we get infinity, but we want to include the correct sign. And since we are dividing a positive number by a negative number by a positive number, I'm sorry, we're going to get positive infinity, right? Two positive numbers give us a positive ratio. So the correct answer to this problem is option B infinity. Thank you for watching.

Determine the following limits.
lim x→3^- x − 4 / x^2 − 3x

Key Concepts

Limits

Continuous Functions

Factoring and Simplifying Expressions

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