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

Asked on by sapon

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

limĀ (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

limĀ (sin x + cos x) = (sqrt3 + 1)/2

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