Solving "Find k if g(x) is Continuous

[hallowon]

Homework Statement

g(x)={x+3, x[STRIKE]=[/STRIKE]3
{2+$$\sqrt{k}$$ , x=3

find k if g(x) is continuous

Homework Equations

The Attempt at a Solution

I have no idea how to begin, but drawing the first part on a cartesian plane.

 

[Gunthi]

Are you sure g(x) is well defined? Because if it is you just have to get a k that doesn't cause a contradiction...

 

[Seb97]

Hi Hallowon
Is the first part not x+3, and x not eual to 3? YA

To say that g(x) is continuous at y=3 is to say that

lim as x goes to 3 = f(3)

In our case the left hand side is equal to x + 3= 3+ 3=6

while the right hand side is equal to 2 + rootk but this must equal the left hand side for it to be continuous so we have

6= 2 + rootk
4=rootk
16=k

Hope this helps. Sorry I had to give solution.haha

 

[hallowon]

ahh thank you i didn't event hink to make them equal to one another. Looks like i have a long way to go for continuity -_-

 

[Seb97]

Ah your welcome. Its actually not that bad. I haven't really covered it but if you have any futher questions don't hesitate to ask. If you look on you tube they might have something on continuity. It would be much more helpful seeing someone go through it rather than reading from some black and white textbook.

 

[Redbelly98]

Hope this helps. Sorry I had to give solution.haha

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