1. ## Calculus Limit Problem

I need help solving the following problem. I need the find the values of m and b.

limit x->0 [(root mx + b) - 3 ] / x = 1

I tried rationalizing this which was multiply by (root mx + b) + 3 on both the denominator and numerator, but then I do not know where to do from here. I cross multiplied the denominator with the 1, and my teacher said it was wrong. Please help!

2. Originally Posted by mathamatics112
I need help solving the following problem. I need the find the values of m and b.

limit x->0 [(root mx + b) - 3 ] / x = 1

I tried rationalizing this which was multiply by (root mx + b) + 3 on both the denominator and numerator, but then I do not know where to do from here. I cross multiplied the denominator with the 1, and my teacher said it was wrong. Please help!
you cannot cross multiply. note that by rationalizing you get

$\lim_{x \to 0} \frac {mx + b - 9}{x(\sqrt{mx + b} + 3)}$

clearly we need $\boxed{b = 9}$ in order to cancel the x in the denominator and find the limit, thus we are left with

$\lim_{x \to 0} \frac {m}{\sqrt{mx + 9} + 3}$

now what?

3. Just a question, How why did you make b - 9 = 0 which turns to b = 9? What will happen to the m?

Also what happened to the 1 on the right side?

What happens to the m on the denominator and the numerator? other than that, Thank you very much because I see the answer.

4. Originally Posted by mathamatics112
Just a question, How why did you make b - 9 = 0 which turns to b = 9?
in order to take the limit, i need to cancel the x in the denominator. to do that, i had to be able to factor out an x from the numerator. to do this, i had to get rid of the -9. thus, making b = 9 i got rid of it.

What will happen to the m?
nothing, yet

Also what happened to the 1 on the right side?
we don't worry about it yet. 1 is what we want the answer to be. so when we are done with the limit and get an expression for it, we equate it to 1 and solve for m

What happens to the m on the denominator and the numerator? other than that, Thank you very much because I see the answer.
take the limit and see what happens...