Question

find the values of the constants a and b such that lim x goes to 0 (square root)a+bx-(square root)3/x=(square root)3

Answer 1

\[\lim_{x\to 0} \frac{\sqrt{a+bx}-\sqrt 3}{x}=\sqrt 3\]
Is this your question?

Answer 2

yes

Answer 3

For the limit to exist, when x goes to 0
Both numerator and denominator should become 0, denominator becomes 0 when x=0
could you equate the value of numerator to zero, plugging in x=0??

Answer 4

no i do not know how to do that

Answer 5

is it just the square root of a+b - the square root of 3?

Answer 6

We have
\[\sqrt{b+ax}-\sqrt {3}=0. For\ x=0\]
put x=0 here
\[\sqrt b-\sqrt 3=0\]
what do you think is the value of b?

Answer 7

That's root b, value of b?

Answer 8

9

Answer 9

if we had
\[\sqrt b=3\longrightarrow b=9\]

\[\sqrt b=\sqrt 3\longrightarrow b=???\]

Answer 10

\[\sqrt{9} ???\]

Answer 11

square both sides, what'd you get for b?