Unit 02 · Foundation Pathway
How can values near an input reveal behavior at that input—even when direct substitution fails?
Khaemenes Academy · Calculus I
Limits: Numerical, Graphical & Algebraic Reasoning · Show reasoning, notation, intervals, units, and corrections.
Evaluate lim x→2 (x²−4)/(x−2), showing the factorization.
Use the lesson example and name the rule before calculating.
Evaluate lim x→3 (x+1). Explain why direct substitution works.
Use the lesson example and name the rule before calculating.
For f(x)=2x+1, calculate f(1.9), f(1.99), f(2.01), f(2.1). Predict lim x→2 f(x).
Use the lesson example and name the rule before calculating.
Evaluate lim x→0 sin(x)/x. State the unit requirement.
Use the lesson example and name the rule before calculating.
If lim x→1⁻ f(x)=2 and lim x→1⁺ f(x)=7, determine whether lim x→1 f(x) exists.
Use the lesson example and name the rule before calculating.
Evaluate lim x→4 (x²−16)/(x−4), for x≠4.
Use the lesson example and name the rule before calculating.
Evaluate lim x→∞ 5/x. Describe the horizontal behavior.
Use the lesson example and name the rule before calculating.
For f(x)=(3x²+1)/(x²−4), find lim x→∞ f(x).
Use the lesson example and name the rule before calculating.
For f(x)=(x²−9)/(x−3), x≠3, identify the missing graph point.
Use the lesson example and name the rule before calculating.
Let f(x)=x+2 when x<1 and f(x)=2x when x≥1. Does lim x→1 f(x) exist?
Use the lesson example and name the rule before calculating.
Explain whether f(a) must equal L whenever lim x→a f(x)=L. Give a counterexample.
Use the lesson example and name the rule before calculating.
Evaluate lim x→0 |x| using left and right approach values.
Use the lesson example and name the rule before calculating.
The printed questions are formative exercises. Passing course mastery checks at 80% is required to unlock the next activity; worksheet completion alone does not grant progression.