find the valye of the constant k that wil make the function continuous- f(X)= {kx^2 , x greater than or equal to 2 and kx-6 , x

Question

find the valye of the constant k that wil make the function continuous- f(X)= {kx^2 , x greater than or equal to 2 and kx-6 , x<2 how would u start this off i understand the concept but i dont know how to start it

myininaya · Answer

use the definition of continuity
you want the limit to exist as x->2
so do left limit and right limit 
and set equal to solve for k

myininaya · Answer

$$\lim_{x \rightarrow 2^-}(kx-6)=\lim_{x \rightarrow 2^+}kx^2$$

myininaya · Answer

$$2k-6=4k$$

myininaya · Answer

solve for k

liizzyliizz · Answer

ooh its that easy why does it seem much more complicated o.o thank you so much

anonymous · Answer

myininaya has that power!

liizzyliizz · Answer

satellite i have a question for u ! :D

liizzyliizz · Answer

regarding the continuity of a piecewise  function where u need to determine the x value where the rule changes