Evaluate each of the following limits. Be sure to show all of your work using methods (algebra, limit properties, and/or logic). If the limit does not exist, show why.

Question

Answer 1

you could do L'hopital's rule, taking derivaties of numerator over derivaties of denominator, enough times to reach a fraction where substituting infinity for x is not undefined

or just notice that the dominant terms will be (sqr7)x/5x = sqr7/5 = the limit as x approaches infinity. the highest degreed terms dominate, and if they are the same degree, their coefficients are the limit

= about 0.529150262

=about one half

or use an online limit calculator such as symbolab