? ? ? ✓ 4. If F = ▼ ƒ, then F is conservative. 5. Sc F · dr = f(Q) – ƒ(P) whenever P and Q are the endpoints of the curve C. F. dr = 0. 6. If F is path-independent and C' is any closed curve, then

For T:R5R3 and nullity(T)=2, find rank(T).

2a. 2b.

Consider a dataset of numbers y1, y2, ..., yn and  the linear function f(x) = 9x − 4.  Prove or find a counterexample to disprove. If a ≤ b, show that f(a) ≤ f(b). since it is a monotonic function that is increasing i was thinking of doing the derivative to prove it but i dont what else to do more to prove it after doing it.

MAT Lalculus... PHY131H1F - Classes 3 / 3 4. The function h satisfies the following equation: Væ E R, h(xh(x)) = [h(x)]* In addition, we know: • The domain of h is R. •h is twice differentiable (meaning that h is differentiable, and h' is also differentiable). • h(1) = 1. • The graph of h does not have a horizontal tangent line at the point with r-coordinate 1. Calculate h" (1). Hint: Use implicit differentiation. amazon arch X W C