# Thread: Find a real number for a continuous function

1. ## Find a real number for a continuous function

How would I go about doing this?

Find a real number f so that: is a continuous function

y = { 3x - 2d if x is less than or equal to zero
{2x^2 + x + 5d^2 if x is greater than zero.

2. ## Re: Find a real number for a continuous function

Originally Posted by IStandAlone99
How would I go about doing this?

Find a real number f so that: is a continuous function

y = { 3x - 2d if x is less than or equal to zero
{2x^2 + x + 5d^2 if x is greater than zero.
do you mean a real number d?

y is clearly continuous on either side of 0 so just pick d to ensure that the value at 0 agrees coming from both sides.

3. ## Re: Find a real number for a continuous function

Yeah I meant d....so if I put x=0....the equation would be: -2d = 5d^2?

yep

5. ## Re: Find a real number for a continuous function

Originally Posted by IStandAlone99
How would I go about doing this?
Find a real number f so that: is a continuous function
y = { 3x - 2d if x is less than or equal to zero
{2x^2 + x + 5d^2 if x is greater than zero.
You want to solve $\displaystyle{\lim _{x \to {0^ - }}}3x - 2d = {\lim _{x \to {0^ + }}}2{x^2} + x + 5{d^2}$

6. ## Re: Find a real number for a continuous function

There are, of course, two correct answers to this.

7. ## Re: Find a real number for a continuous function

I'm feeling extremely stupid...how would I solve: -2c = 5c^2?

8. ## Re: Find a real number for a continuous function

$5c^2=-2c$
$5c^2+2c=0$
$c(5c+2)=0$

I think you can you manage it from here