Category Archives: Tangent Line

Tangent Lines as Linear Approximations

1. Motivation. So we have some procedure to construct a line tangent to a curve at a given point. What good is it? Well, suppose we want to compute . What is it? I don’t know! Lets introduce the function … Continue reading

Posted in Approximation, Calculus, Differential, Tangent Line | Tagged | 4 Comments

Exponential Function

So we threw down a challenge at the end of our discussion of Tangent Lines, lets solve it. Recall we wanted to find a curve such that for any we have the line tangent to that point satisfy . (Historical … Continue reading

Posted in Exponential Map, Tangent Line | 4 Comments

Line Tangent to a Curve

1. Overview. Suppose we have a line in the plane . What data do we need to specify a line? We need a slope and a point on the line . Then we can specify completely by the equation (1) … Continue reading

Posted in Calculus, Differential, Tangent Line | 5 Comments