Investigating Limits: What Happens When x Approaches a Constant or Zero?

Thread starter nycmathguy
Start date Jun 17, 2021

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SUMMARY

This discussion focuses on evaluating limits in calculus, specifically lim f(x) as x approaches 3 and lim f(x) as x approaches 0. The participants emphasize the importance of understanding the behavior of functions near these critical points. The thread suggests that mastering these limits will enhance overall comprehension of calculus concepts, particularly in relation to continuity and differentiability.

PREREQUISITES

Understanding of basic calculus concepts, including limits and continuity.
Familiarity with function behavior near critical points.
Knowledge of the epsilon-delta definition of limits.
Experience with graphing functions to visualize limits.

NEXT STEPS

Study the epsilon-delta definition of limits in detail.
Practice evaluating limits using L'Hôpital's Rule for indeterminate forms.
Explore the concept of one-sided limits and their significance.
Learn about continuity and its relationship with limits in calculus.

USEFUL FOR

Students of calculus, mathematics educators, and anyone looking to strengthen their understanding of limits and their applications in mathematical analysis.

Jun 17, 2021

nycmathguy

Homework Statement: Investigate each limit.

Relevant Equations: See attachment of piecewise function.

Investigate each limit.

1. lim f(x) x→3

2. lim f(x) x→0

See attachment.

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Jun 17, 2021

Mark44

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Thread closed. This is nearly identical to your other thread with almost the same name. When you figure this one out, you'll be able to figure this one out.