lim 3+2x+4x^2/x^2
x-inf

I know as x approaches inf the x^2 will increase much faster making the lower degree terms insignificant. thats where I am stuck

Question

lim          3+2x+4x^2/x^2  
x->inf

I know as x approaches inf the x^2 will increase much faster making the lower degree terms insignificant. thats where I am stuck

anonymous · Answer

End behavior model of the numerator:$$x^2$$End behavior model of the denominator:$$x^2$$Restatement of the limit approaching infinity:$$\lim_{x\rightarrow\infty}\dfrac{x^2}{x^2}=\lim_{x\rightarrow\infty}1=1$$

anonymous · Answer

I thought as much its just that I wasn't sure if you could cancel the variables like that thanks

anonymous · Answer

You can because with extremely large values of x, the numerator and the denominator are essentially equal, and thus the quotient will be basically 1.

anonymous · Answer

what about the 4 in the 4x^2

anonymous · Answer

Ach!  My apologies!  I missed seeing that.  You are right!  We thus have $$\lim_{x\rightarrow\infty}\dfrac{4x^2}{x^2}=4$$Good spotting!  Do watch out for those! :)

anonymous · Answer

got it thanks

anonymous · Answer

I got another question I will post it so you can get another medal