Crash course in limits (1 Viewer)

[-pari-]

can someone please help me understand limits/continuity?

things like,

for eg, if given the function y = (9 + x^2)/3x
how do you "determin the limits of the function as x --> 0, x--> positive/negative infinity"

?

 

[watatank]

I'm a little rusty, but I draw a graph of that.

As x tends to zero, replace all x's for zeros to find the limit....so the limit is where the function is undefined (as the denominator cannot be zero), so there is an assymptote on x = 0 ie the y axis.

the y assymptote is your limit as x tends to +-infinity....as x gets bigger, you can pretty much forget about the 9 in the numerator...so to find the limit as x tends to infinity you only consider all degrees (highest powers) of x in numerator and denominator.

the y assymptote becomes (x^2)/3x = x/3

Ok so you know your assymptotes now plot points and draw the graph and hopefully that answers your question