Question

limit of x---> infinity
(x + 2)/sqrt(49x^2 + 1)

Answer 1

forget the 1 under the square root, the 2 in the numerator, and compute
\[\frac{x}{\sqrt{49x^2}}\]

Answer 2

\[\lim_{x \rightarrow \infty}\frac{(x+2)}{\sqrt{49x ^{2}+1}}\]\[\lim_{x \rightarrow \infty}\frac{\frac{(x+2)}{x}}{\frac{\sqrt{49x ^{2}+1}}{x}}\]\[\lim_{x \rightarrow \infty}\frac{1+\frac{2}{x}}{\sqrt{49+\frac{1}{x ^{2}}}}\]Reaplace the value infinite:\[\frac{1+0}{\sqrt{49+ 0}}\]\[\frac{1}{7}\]

Answer 3

that will work for sure, but
\[\frac{x}{\sqrt{49x^2}}=\frac{1}{7}\] is somewhat quicker

Answer 4

thats true :)