What is the tangent line approximation for e^x near x=0

Question

What is the tangent line approximation for e^x near x=0

 

Answer 1

The tangent line approximation would include the point (0,1) since e^x goes through it.

 

To find the tangent line, we would also need to find the slope.  We can do this by taking the derivative of y = e^x and evaluating it at x = 0.

 

y' = dy/dx = e^x

 

slope = e^x|_x=0 = 1

 

 

Equation of tangent line through (0,1): y - 1 = 1(x - 0)

 

y = x + 1