Question

Calculate the limit
limit x->infinity 2x^2 + 100 / x^2 +1

I am not sure how to do this.
I am not sure if you actually mean
limit x->infinity (2x^2 + 100) / (x^2 +1).

If that's the case, parentheses are required (and not optional) :(

When evaluating the limit of a rational function to infinity, check the leading terms (i.e. term raised to the highest power) of the numerator and the denominator.

If they are to the same degree (i.e. raised to the same power), then the limit is the quotient of the coefficients, in this case 2x²/x² = 2.


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