Explain why the approximation 1016 asymp 106 is reasonable

Question

1. Find the linearization of the function f(x) = x⁴ + 3x² about the point x = -1.

2. Find the linearization of the function f(x) = sin (x) about the point x = π/3.

3. Use the linearization of the function f(x) = sin (x) about the point x = 0 to approximate sin 1^o.

4. Explain why the approximation (1.01)⁶ ≈ 1.06 is reasonable.

5. Find all of the critical numbers of the function f(x) = |sin(πx/2)|