Calc- limits
show your method

A. Factor the numerator as a difference of squares:



c. As , the contribution of the terms of degree less than 2 becomes negligible, which means we can write



e. Let's first rewrite the root terms with rational exponents:



Next we rationalize the numerator and denominator. We do so by recalling




In particular,




so we have



For and , we can simplify the first term:



So our limit becomes

6(2x + 5y)6 (2x) = 12x6 (5y) = 30y12x + 30y