Find the limit algebraically. lim √x+16 −4/x as x approaches 0.

Question

Note that it says the square root of x+16.

Answer 1

I think that you mean lim_x→0 [(√(x+16) - 4) / x]. If so, this limit has the indeterminate form 0/0.

Multiply and divide by √(x+16) + 4 to get:

lim_x→0 [x / (x(√(x+16) + 4))] = lim_x→0 [1 / (√(x+16) + 4)] = 1 / 8