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

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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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