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Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

f(x)={2x+k,x<310,x=3x2+1,x>3f(x)=\begin{cases}2x+k,&x<3\\10,&x=3\\x^2+1,&x>3\end{cases}
Total: 5 points

(a) Find lim⁡x→3−f(x)\lim_{x\to3^-}f(x) in terms of kk. (1 point)

(b) Find lim⁡x→3+f(x)\lim_{x\to3^+}f(x). (1 point)

(c) Find the value of kk that makes ff continuous at x=3x=3, or explain why none exists. (3 points)

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