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...Dierent types of limits besides ordinary two sided there are one left hand and right innite at innity consider limx x might think that since as it would follow lim but when is close to smaller than undened for some values very the limit doesn t exist we still like a way saying so say exists write approaches from sometimes have not sometimeswehavebothleft handandright handlimitsandthey re same both they equal in which case example if f while suppose interested estimating about how big xis s easy see ifx thus will be similarly small here does mean means negative number with large magnitude absolute value calculating aconvenient nd quotient or minus factor out largest term numerator denominator cancel what can obvious atechnicality technically function an actually has specic inferred fairly intuitively may look g positive then variations also inn ity asymptotes l y horizontal asymptote c vertical...