5) Find the divergence of (√x² + y² + )(i + y + zk)

Find and sketch the domain of f(x, y) = √√₁ - (x + 1)² − y² + 2ln(x − y + 1)

Consider the function 2² + 2x +1 y = r2 +1 a) Show that the domain of this function is a €R. b) Find the points where the function y = f(x) intersects the r-axis and the y-axis. c) Show that dy 2 – 212 %3D dr (포2 + 1)2' and dy 4r(r2 – 3) (교2+ 1)3 %3D dr? d) Locate and classify the critical points of the function y = f(x). e) Locate any inflection points of the function y = f(x). f) Find the limits of the function y = f(r) as r→ too. g) Using your results from Parts a to f, draw a sketch of the function y = f(x), clearly indicating the r- and y-intercepts, any critical points and inflection points, and its behaviour for x+ t0o.

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