Question

for what value of k for the following fn : continuous at x= - pi/6

f(x) = { root 3 sinx + cos x / x+ pi/6 ; x is not equal to - pi/6

k ; x = - pi/6

Answer 1

when x not equal to pi/6
√3 sinx + cosx=1/2(√3/2 sinx +1/2 cosx)
=1/2 (cos(pi/6)sinx+sin(pi/6)cosx)
=1/2 sin(x+pi/6)
limit x->- pi/6 ( 1/2 (sin(x+pi/6)/(x+pi/6))=1/2
for continuity k=1/2

Answer 2

Answer:

K=2

Step-by-step explanation:

for what value of k for the following fn : continuous at x= - pi/6

f(x) = { root 3 sin x + cos x / x+ pi/6 ; x is not equal to - pi/6

          k                                             ; x = - pi/6