Determine the following limits.
lim x→5 x − 7 / x(x − 5...

Question

Determine the following limits.

lim x→5 x − 7 / x(x − 5)^2

Accepted Answer

Welcome back, everyone calculate the limit limit of X minus four divided by X multiplied by X minus three squared. When X approaches three were given four answer choices A zero B infinity C negative infinity. And D one, we can begin solving this problem by direct substitutions. We have limit. When X approaches we of X minus four divided by X multiplied by X minus three squared. Applying direct substitution, we get three minus four which is negative one. And in the denominator, we get three multiplied by three minus three squared. Now three minus three squared essentially gives us zero squared, right. It doesn't matter if we approach three from the left or three from the right because we have that square. So either we get zero negative squared or zero positive squared, that's basically zero squared, right as a positive valley. So it is really important to understand that we can simplify that to negative one divided by three multiplied by zero squared, which is essentially zero from the positive side G to that square, right. Remember that whenever we, we square a positive or a negative number, we get a positive number. Now, whenever we take a limit of a number divided by zero, we get infinity, right? Because we are dividing a number by an infinitely small number. Since we are approaching zero from the right, we're going to get negative one divided by zero positive, which essentially means that we get infinity with a negative sign due to that negative sign in front, right? That's really important. So the answer to this problem, what corresponds to the answer to ac negative infinity? Thank you for watching.

Determine the following limits.
lim x→5 x − 7 / x(x − 5)^2

Key Concepts

Limits

Indeterminate Forms

L'Hôpital's Rule

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