What are the asymptotes of the function #f(x) = x+1+sin(x^2)/x# ?
1 Answer
Nov 20, 2017
See explanation...
Explanation:
Note that for any real value of
So:
#abs(sin(x^2)/x) <= abs(1/x) -> 0# as#x->oo#
So the function:
#f(x) = x+1+sin(x^2)/x#
tends to the line
However, note that whenever
Hence the function
Some definitions of asymptote preclude the intersection at infinitely many points, but most modern definitions allow it.