Does the graph of

have a tangent at the origin? Give reasons for your answer.

We say that a continuous curve y = ƒ(x) has a vertical tangent at the point where x = x₀ if the limit of the difference quotient is ∞ or -∞. For example, y = x1/3 has a vertical tangent at x = 0

However, y = x²/3 has no vertical tangent at x = 0

does not exist, because the limit is q from the right and -∞ from the left.

Transcribed Image Text:

g(x) = xsin (1/x), x0 0, x = 0