Grade 11 Maths Limits Question-Please Help!?

Question

Hey I'm doing grade 11 maths here and I'm stuck on limits, I was wondering if anybody could explain to me with some examples if possible how to do the following questions.

Evaluate the following limit

14x + 7

----------- x --> -1/2

2x + 1

and

limit

x^2 - 9x - 10

------------------ x---> -1

x + 1

I know in these questions the bottom line becomes 0 so you have to do something to the top line but i dont really understand. If someone could explain it to me and possibly put an example up that would be sooo helpful!...Thankyou in advance...

Btw the dotted lines is divided by...or over or whatever you want to call it

Answer 1

The first one is simple. Don't get thrown off by plugging in -1/2 and getting an undefined answer. The degree on the numerator and denominator are both 1 (x = x^1) so when you graph it, you will get a horizontal line. (14x)/(2x) = 7. The + 7 and + 1 in the numerator and denominator are negligible when you approach infinity so we just discard them. The limit as x approaches any number for this equation will always equal 7 because the equation is y = 7. Is this making sense?

lim as x --> -1/2 (14x + 7) / (2x + 1) = 7

The second one is where you must factor the numerator because plugging in -1 you get an undefined answer:

(x^2 - 9x - 10) / (x + 1)

[(x + 1)(x - 10)] / (x + 1)

The (x + 1)'s cancel out and you're left with:

x - 10

The lim as x --> -1 of (x - 10) = -11.