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An introduction to limits: the gateway idea of calculus — Homework
Build a table of values approaching the target from both sides whenever a limit feels uncertain, and check all three continuity conditions in order.
- 1.Evaluate lim as x approaches 5 of (x^2-25)/(x-5).
- 2.Evaluate lim as x approaches 3 of (x^2+2x-1) directly.
- 3.Evaluate lim as x approaches infinity of (5x^3+2)/(2x^3-x+1).
- 4.A function is defined as f(x) = {x+1 if x<2; 5 if x=2; x+3 if x>2}. Does lim as x approaches 2 of f(x) exist? Is f continuous at x=2? Explain.
- 5.Evaluate lim as x approaches infinity of (4x+1)/(x^2-3), and explain which degree-comparison case applies.
🌲 Homeschool of the FutureTwelfth Grade · Math · week 36 homework