Evaluate the limit of sin x + cos x, if x->pi/3?
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
To find the limit of sin x + cos x for x--> pi/3, we first substitute x with pi/3 to see if we get a valid solution.
sin x + cos x for x--> pi/3
=> sin (pi/3) + cos (pi/3)
we see that both sin (pi/3) and cos (pi/3) are defined.
sin (pi/3) = (sqrt 3) /2
cos ( pi/3) = 1/2
sin (pi/3) + cos (pi/3) = (sqrt 3 + 1)/2
Therefore the required limit is (sqrt 3 + 1)/2
giorgiana1976 | College Teacher | (Level 3) Valedictorian
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