Suppose limh->0 (f(h)-f(0))/h =+infinity and f(0)=0. What kind of feature can best explain this?

Question

a)such scenario is not possible

b)f(x) has a vertical tangent at x=0

c)f(x) must be discontinuous at x=0

d)f(x) has a vertical assymptote at x=0, and f(0) is defined to be 0.

 

I tried a) and b) but they are not correct.

 

what is the right answer?

Answer 1

The limit represents the slope of a line (or the tangent at a point on a curve)

Since slope = rise/run which is infinity for this case.

That means the run or h --> 0.

This represents a vertical asymptote. 

So the correct answer is d).