Assignment:
The first problem deals with finding the circumference length of an ellipse. This field is called differential geometry. The second problem deals with finding the equation of tangent line of a given equation.
Q1. Find the circumference length of an ellipse:
X^2 / 4 + y^2 / 9 = 1
Q2. Find the equation of tangent line at (x=2, y=13) of the following equation:
Y = x^3 + x^2 +1
a) Find the slope then determine the equation of tangent line.
b) Define f = x^3 + x^2 + 1 - y
Use ∇f to determine the normal vector then use "vector dot product" method to find the tangent line equation.
Provide complete and step by step solution for the question and show calculations and use formulas.