Demand 1 Outline a characteristic 𝑓: ℝ2 ⟶ ℝ2 by (a) Resolve the cost of k for the characteristic 𝑓 to be real at (0, 0), if any. (Exercise this label of k for the next sub-questions.) (10 marks) (b) Instruct that 𝑓𝑥 (0, 0) and 𝑓𝑦 (0, 0) both exist and web their values. (10 marks) (c) Outline 𝑓𝑥 (𝑥, 𝑦) and 𝑓𝑦 (𝑥, 𝑦) each and every as a piecewise characteristic within the total domain of ℝ2 (12 marks) (d) Hence or otherwise, camouflage whether the characteristic 𝑓 is differentiable at (0,0). (18 marks) Write My Task Rent a Professional Essay & Task Creator for finishing up your Academic Assessments Native Singapore Writers Crew 100% Plagiarism-Free Essay Very most life like Pride Payment Free Revision On-Time Offer Demand 2 A GPS application designed for hikers measures the altitude, z, at varied positions on a terrain and performs a regression, yielding the altitude characteristic below, where x, y and z are measured in km. (a) Advise an equation that describes the stage living of the characteristic and utilize it to space the contours of the terrain at the altitudes of 1.3 km, 1.5 km and a number of km with a graph plotter. Set aside a screenshot of the graph and label each and every contour with its equation clearly. (8 marks) (b) A hiker crosses the blueprint (0, 1) whereas walking alongside a contour. Resolve the contour equation and calculate the gradient vector of the terrain characteristic at the blueprint (0, 1). Instruct that this gradient vector is orthogonal to the contour at the blueprint (0, 1). (18 marks) (c) A hiker is walking alongside a course given by 𝑦 = 1 − 𝑥 − 𝑥 3 Sketch the path on your graph in portion (a) and compute the directional derivative alongside the path at (0, 1) within the direction of increasing altitude. Screech briefly the which implies of this label of the directional derivative. (10 marks) (d) The GPS carried by the hiker in portion (c) reveals that his ground bustle is 0.8 m/s. Compute the charge of ascent (with admire to time) of the hiker as he crosses (0, 1). What’s the level of slope and the diagram in which like a flash is he walking within the upslope direction? (7 marks) (e) One other hiker is planning to lunge from (5/2, 5/4) to (4, 2) in a straight line. From the contours plotted in portion (a), camouflage the terrain he’ll abilities alongside this course (with out using calculations). (7 marks) Buy Personalized Resolution of This Overview & Elevate Your Grades Salvage A Free Quote
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