Find lim𝑥→4𝑓(𝑥) for the given piecewise function. lim_(x->4)f(x)={(2x+2 IF x<4),(3 IF x-4),(-(1)/(2x)+12 IF x>4)}

Question

lim𝑥→4𝑓(𝑥)=

Answer 1

Hi,

f(x)={(2x+2 IF x<4),(3 IF x-4),(-(1)/(2x)+12 IF x>4)}

lim𝑥→4𝑓(𝑥)=

For finding limit of piecewise function:

you need to make left and right at 𝑥→4

for 𝑥→4⁺ see that part of function that domain is x>4 then plug in x = 4, IN THIS CASE f(x) = -

-(1)/2(x)+12

=𝑥 →4⁺======> -1/2(4) + 12

for 𝑥→4^- see that part of function that domain is x<4 then plug in x = 4 IN THIS CASE f(x) = 2x+2

 lim 𝑥→4^- =====> 2(4) + 2

if you find the same answer for 𝑥→4^- and 𝑥→4+ there is limit of function when 𝑥→4

I hope it was useful.

Minoo