Question

Evaluate the limit.

(Use symbolic notation and fractions where needed.)


\[\lim\limits_{x \to \infty} [\frac{1}{x}-\frac{6}{x+53}] = \]

Answer 1

hi @rjo89 :)

try substuting, x = 1/y

then 1/x =... ?

and since x->infinity, 1/x -> ....?

Answer 2

thanks! the answer's 1

Answer 3

oh, is it! ??
i got the answer as 0

how did u get it as 1 ?

Answer 4

\(\dfrac{1}{x} - \dfrac{6}{x+53} = \dfrac{x+53 - 6x}{x(x+53)} = \dfrac{53 - 5x}{x^{2} + 53x}\)

And thus we see rather clearly that the limit as x increases without bound is 0. I, too, would be quite interested to see how '1' was obtained.