MAT 1234 Calculus I Sage Math Lab 2

MAT 1234 Calculus I Sage. Math Lab 2

Good Practices for HW l l l Use only pencils. Use pencils to write down complete solutions to your homework problems in a notebook or loose papers in a binder. The key word here is “complete”. You want to have a good record to study for the exams.

Grading Comments l l Please read the instructions! Please label your graphs Figure 1 Graphs of �� =sin���and �� =cos��� on [0, 2 ]

Lab 2 Objectives l l l To develop an intuitive understanding of the nature of limits. To lay the foundation for the frequent use of limits in calculus. To experience the power and peril of investigating limits by successively closer evaluation.

Due Date l (See Canvas)

Instructions Round off to 5 decimal places l Give full Answers Example: What is ? l

No Calculators l l l You are expected to use Sage. Math. Do not use phones, calculators, apps, or other internet resources. BTW, make sure you have an approved calculator by Friday (see syllabus).

Define functions

Define functions f(x)=x^2+x-1; show(f(1)); show(f(2));

Define piecewise functions

Define piecewise functions g(x)=piecewise([[(-infinity, 1), 1], [(1, infinity), x]]); plot(g(x), (x, -2, 2), ymin=0, ymax=2);

Reminders l l l Give full Answers: Please label your graphs: , not just . Define a function and evaluate function values: f(x)=x^2+x-1; show(f(1)); show(f(2)); l Define a piecewise function: g(x)=piecewise([[(-infinity, 1), 1], [(1, infinity), x]]); plot(g(x), (x, -2, 2), ymin=0, ymax=2);