# Calculus Examples

Verify the Existence and Uniqueness of Solutions for the Differential Equation
,
Step 1
Assume .
Step 2
Check if the function is continuous in the neighborhood of .
Substitute values into .
Substitute for .
Substitute for .
Subtract from .
There is an even radical with a zero as the radicand, which means that the function is not continuous on an open interval around the value of .
Not continuous
Not continuous
Step 3
The function is not continuous on an open interval around the value of .
A solution is not guaranteed