Thread: finding a number so that f is continuous at every point

1. finding a number so that f is continuous at every point

Good evening everyone need some help with this problem i got wrong, have an exam tomorrow and i'm trying to figure this out. Thanks in advance!

2. Originally Posted by tecknics
Good evening everyone need some help with this problem i got wrong, have an exam tomorrow and i'm trying to figure this out. Thanks in advance!

$\lim_{x \to -5^-} f(x) = \lim_{x \to -5^+} f(x) = -12$

and

$\lim_{x \to 1^-} f(x) = \lim_{x \to 1^+} f(x) = 12$

you'll get two equations in terms of $a$ and $b$ ... solve the system.

3. Originally Posted by skeeter
$\lim_{x \to -5^-} f(x) = \lim_{x \to -5^+} f(x) = -12$

and

$\lim_{x \to -5^-} f(x) = \lim_{x \to -5^+} f(x) = 12$

you'll get two equations in terms of $a$ and $b$ ... solve the system.
I know how to do that part you just showed, but as far as the next step im lost

4. $\lim_{x \to -5^-} -12 = \lim_{x \to -5^+} ax+b$

$-12 = a(-5)+b$

$\lim_{x \to 1^-} ax+b = \lim_{x \to 1^+} 12$

$a+b = 12$

solve the system

5. Originally Posted by skeeter
$\lim_{x \to -5^-} -12 = \lim_{x \to -5^+} ax+b$

$-12 = a(-5)+b$

$\lim_{x \to 1^-} ax+b = \lim_{x \to 1^+} 12$

$a+b = 12$

solve the system
That makes sense to me now, but now i'm lost for solving the system, i was in Iraq for a year and completely forgot about everything math related and need to practice some more.

6. Wooo, i got it just now thank you very much!