Question

calc! :( Please help me!! The question is attached. It involves discontinuity.

Answer 1

you want the end points of each region to "match up"
in other words as x gets close to 2
you want 3x+5 to approach the same value as c x^2 +d
3x+5 = c x^2 +d as x-> 2
if we put in x=2 we get
3*2 + 5 = c*(2^2) + d
which simplifies to
11 = 4c + d

similarly, as x->1 we want

4x + 4 = c x^2 +d as x->1

can you simplify that equation? what do you get ?

Answer 2

Do I have to find the limit of that function as x approachs 1?

Answer 3

I substituted 1 for x and got that 8=c+d

Can I set up a systems of equation with the equations 8=c+d and 11=4c+d

Answer 4

When I create the systems, I get that c=1 and that d=7

Is that correct?

Answer 5

yes, exactly
you could subtract them.

yes c=1 and d=7
which makes the middle expression x^2 + 7

Answer 6

Thank you!! I understand it! :)

I have another problem, if you have time. I started doing the problem, but I don't know how to finish it. it number 1 on the ws.

Answer 7

for Q1, your answer
\[ \frac{1}{2\sqrt{x+3} }\] is correct.