Evaluate the limit of sin x + cos x, if x->pi/3?

We'll evaluate the limit of the sum of the functions sine
and cosine in this way;

lim (sin x + cos x) = lim sin x +
lim cos x, x-> pi/3

We'll substitute x by the value
of pi/3 and we'll get:

lim sin x + lim cos x = lim sin pi/3
+ lim cos pi/3

sin pi/3 =
sqrt3/2

cos pi/3 = 1/2

lim sin
x + lim cos x = lim sqrt3/2 + lim 1/2

The limit of a
constant function is the value of the constant:

lim sin x +
lim cos x = sqrt3/2 + 1/2

lim (sin x + cos x)
= (sqrt3 + 1)/2