Assignment:
Q1. For the equation ƒ(x)= x^(1/2)
a) Find the Taylor polynomial of degree 4 of at c = 4
b) Determine the accuracy of the polynomial at x = 2.
Q2. Find the Maclaurin series in closed form of
a) ƒ(x)=((1) / ((x+1)^2)
b) ƒ(x)=ln ((x^2)+1)
Q3. Use the chain rule to find dw / dt, where w = x^2 + y^2 + z^2, x=(e^t) cos t, y=(e^t) sin t, z=(e^t), t=0.
Q4. Find the critical points and test for relative extrema: ƒ(x,y)=2(x^2)+2xy+(y^2)+2x-3
Q5. Maximize ƒ(x,y)= (6-(x^2)-(y^2))^(1/2) given the constraint x+y-2=0.
Provide complete and step by step solution for the question and show calculations and use formulas.