Question

HELP PLEASE! CALC limits- find a and b such that :

Answer 1

There are many ways of solving for limits. The easiest way is to directly plug in the x value that the graph is approaching. While you're not looking for the limit in this question, you should still be plugging in that x value, 3, to help create an equation for you to solve for a and b!

So start by plugging in 3 for x. Once you do that, you can get rid of the pesky lim notation, so from then on it would be algebra:
$\frac{-2+ \sqrt{3a+b} }{3} = 1$

Now isolate the variables a and b by multiplying by 3 on both sides, adding 2 on both sides, and then squaring both sides:
$\frac{-2+ \sqrt{3a+b} }{3} = 1$
$-2+ \sqrt{3a+b} = 3$
$\sqrt{3a+b} = 5$
$3a+b = 25$

Since you're not given any other information, I'm assuming you can probably just put in random numbers that work for a and b so that it equals 25. For example, a = 5 and b = 10.