lim x tends to infinity (x+sin x/x-cos x)1/2 lim x tends to infinity (sin x -cosx)/x - Maths - Limits and Derivatives

Question

lim x tends to infinity (x+sin x/x-cos x)1/2
lim x tends to infinity (sin x -cosx)/x

Prasanta · Accepted Answer

(1) limx→∞x+sinxx-cosx

=∞+a number lying between -1 and 1∞-a number lying
between -1 and 1

=∞+0-a number lying between -1 and 1

=∞

(2) limx→∞sinx-cosxx

=limx→∞sinxx-limx→∞cosxx=a number lying
between -1 and 1∞ - a number lying between -1 and
1∞

=0-0=0