Unsure where to start with finding value of 'a' in limit calculation

[avanm]

Hi there,
Im super unsure how to start this question. I know that lim_x->a f(x) can be either inf, -inf, or DNE when given the lim_x->af(x) and if f(a)=nonzero#/0 but im unsure where to go from there.

I want to factor the top and have it cancel with the bottom but then what I wrote above wouldn't be true (nonzero/0). Could someone suggest a route I can go, or direct me to a similar video solving something like this?

Greatly appreciated and thank you !

 

[Dr.Peterson]

This is not a routine problem; it makes you use the knowledge you've gained from more routine examples. So showing you a trick would not help you learn from it.

I suggest you start with some examples, if you have nothing else to try. Suppose a = 1, or 2, or 3; what will the limit be? Then you can think about what makes the difference, and will have more ideas for solving the actual problem.

 

[Steven G]

If the numerator is a non-zero constant or is approaching a non-zero constant AND the denominator is approaching 0, then the fraction is approaching +infinity or -infinity. Which infinity depends on the sign of the fraction.

 

[avanm]

This is not a routine problem; it makes you use the knowledge you've gained from more routine examples. So showing you a trick would not help you learn from it.

I suggest you start with some examples, if you have nothing else to try. Suppose a = 1, or 2, or 3; what will the limit be? Then you can think about what makes the difference, and will have more ideas for solving the actual problem.

If the numerator is a non-zero constant or is approaching a non-zero constant AND the denominator is approaching 0, then the fraction is approaching +infinity or -infinity. Which infinity depends on the sign of the fraction.

From what I gather the question is asking what values if any does the limit(s) equal to inf/-inf.

So if the numerator is a non-zero constant or is approaching a non-zero constant and the denominator is approaching 0, then the fraction is approaching +infinity or -infinity.
With that being said, if you need the numerator to approach a nonzero then 'a' can be any number but 'a' ≠ -2, -3
Also since were approaching from the right then the denominator will always be positive and to have the function equal to +inf then the numerator will need to be positive so the interval will be (-1,inf) for the limit approaching inf+ to equal inf. ( figured out the domain by plugging in descending x values till the numerator either became negative or zero)

and for it to equal neg inf itll be the interval (-1, -inf) aka every number that will make the function negative.

Is that correct? or is there calculations I need to write?

 

[Steven G]

a - more than a will be NEGATIVE. That is as x approaches a from the right, a-x will be negative.

It seems that you are trying to do both parts at the same time. Please do them separately.

For part a what must be true about x^2 + 5x + 6? When is that true?
For part b what must be true about x^2 + 5x + 6? When is that true?

Please don't write (-1, - infinity) as the left number should be the smaller number. Please graph x^2+5x+6 and post the graph with your solution.