MHB What are the values of $a$ and $b$ in this limit?

[karush]

$$\lim_{{x}\to{0 }}\frac{\sqrt{ax+b}-2 }{x}=1$$
Find $a$ and $b$

Clueless!

 

[Greg]

For the limit to exist, that expression must be of the form 0/0, so b = 4. Now use L'Hopital's rule to finish up.

 

[karush]

so at dx $0/0$ the denominator goes to $1$ then

dx of $\sqrt{ax+4}-2$ is $\frac{a}{2\sqrt{ax+4}}$

$x\to0$ $\frac{a}{2\sqrt{4}}=1$ $a=4$

actually can't $a$ be anything

 

[Greg]

Are there any other solutions to the equation $$\frac{a}{2\sqrt4}=1$$?

 

[karush]

no quess not.