Let are two derivable functions of .
Tangent Line of a Graph at a Point
Slope of tangent i.e.
is continous at , i.e. as i.e. as i.e exists, where is called the tangent line to the curve at .
The tangent line of a function at the point is:
(i) The line through with slope if .
(ii) The line if .
It holds when
L’ Hospital’s Rule
It is pronounced “lopital”. The limit when divide one function by another is the same after we take the derivative of each function, i.e.
(iii) , if is finite.
(iv) is not defined, if .
(v) iff or and are finite.