Question

Evaluate lim x → ∞ (√x^2+x+1-√x^2+1)​

Answer 1

Step-by-step explanation:

mx→1+x−1−−−−−√2x2−1=limx→1+x−1−−−−−√2(x−1)⋅(x+1)=

limx→1+x−1−−−−−√2x−1−−−−−√2⋅x−1−−−−−√2⋅(x+1)=limx→1+1x−1−−−−−√2⋅(x+1)=

limx→1+11+−1−−−−−−√2⋅(1++1)=

limx→1+10+−−√2⋅(2+)= ∞.

So

limx→1+x−1−−−−−√2x2−1≠limx→1−x−1−−−−−√2x2−1

And

limx→1x−1−−−−−√2x2−1 does not exist.

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