Limits question

Question

Limits question

tylerd · Answer

$$\lim_{t \rightarrow 5}\frac{ 4t^2-100 }{ t-5 }$$ = 40?

myininaya · Answer

so I assumed you tried factoring the top and got (2t-10)(2t+10)=2(t-5)(2t+10)?

tylerd · Answer

actually no but i should have

myininaya · Answer

what did you do ?

tylerd · Answer

the cheapo way, plugged numbers in coming from both positive and negative sides like 5.01 and 4.99

myininaya · Answer

lol

myininaya · Answer

try the factoring way much faster
and it will confirm your answer you got numerically

tylerd · Answer

one more question

tylerd · Answer

when im finding vertical asymptotes...ah nevermind ill figure it out.

tylerd · Answer

$$f(x)=\frac{ x^2-9x+14 }{ x^2-5x+6 } = \frac{ x-7 }{ x-3 }$$
find vertical asymptotes.$$x \rightarrow 3^- = +oo$$
.$$x \rightarrow 3^+ = -oo$$

but why wouldnt i consider x->7? seems to me that as the numerator gets smaller and smaller f(x) becomes infinitely small?
.$$x \rightarrow 7^- = +oo$$

.$$x \rightarrow 7^+ = -oo$$

tylerd · Answer

i c

myininaya · Answer

as x approaches 7 the top approaches 0 so we have
0/not 0 =0

myininaya · Answer

like so we don't have the limit is positive or negative infinity there

myininaya · Answer

the other you wrote about x=3 looks good