What value of k makes the following function continuous?

Question

f(x) =

(sin(-6x))/(9x). x is less than 0

3x-9k-6. x is greater than or equal to 0

Help!?

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Answer 1 · 2017-12-08T09:56:45

#k = 16/27#

At #x=0# we have

#lim_(x->0)(sin(-6x))/(9x) = -2/3lim_(x->0)sin(6x)/(6x)=-2/3#

at #x=0# we have also

#3 xx 0-9 xx k-6 = -2/3 rArr k = 16/27#