U10 Limits and Continuity(KA/PRE/U10)

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Unit 10: Limits and Continuity 🎓

Defining Limits and Using Limit Notation

👉 Limit means what a function is "getting close to" as x gets close to a certain value.

Example notation: limx → 2 f(x) = 5 means "as x approaches 2, f(x) approaches 5."

Estimating Limits from Graphs

We can look at a graph to guess what the limit is! Let's try with this example:

Exploring Types of Discontinuities

Sometimes a function "jumps" or has a "hole." These are called discontinuities.

Defining Continuity at a Point

A function is continuous at x = a if: ✅ f(a) is defined ✅ limx → a f(x) exists ✅ limx → a f(x) = f(a)

Connecting Infinite Limits and Vertical Asymptotes

When a function goes up or down forever near a certain x-value, we call this an infinite limit and the graph has a vertical asymptote.

Quiz: Test Your Understanding!

If a function jumps at x = 3, what kind of point is this?

  1. Continuous point
  2. Jump discontinuity
  3. Infinite limit

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