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MATH 157

Limits, one idea at a time.

Ten short steps on a live graph, from “what does approaching mean?” to continuity. Then test yourself with quiz-style questions and worked steps.

Part 1 · What a limit is · Step 1 of 10

A limit asks where the graph is heading

from the leftfrom the rightthe hole at height 3
01234−10123456f(2) = 4

Slide x toward 2 from both sides and watch the height f(x). It closes in on 3. The filled dot at height 4 is f(2) itself, and the limit never looks at it: it only cares about x near 2, never x = 2.

Try it: Drag the slider to the right. Both points squeeze toward the open circle, not toward the dot above it.
How close x is to 2± 1
farvery close
f(1)
2.5000
f(3)
3.5000
Gap to 3
0.5000
1.9
2.9748
1.99
2.9975
1.999
2.9997
2.001
3.0003
2.01
3.0025
2.1
3.0252
limx2 f(x) = 3
Read: as x approaches 2, f(x) approaches 3. f(2) = 4 is a separate question.
Quiz yourself

Practice like it is the real quiz

Type your answer, or tap ∞, −∞ or DNE. Stuck? Open the steps one line at a time.

Score
0 / 0
Reading a graphQuestion 1 of 19
Use the graph of f below (the continuity graph from class). Find limx−4 f(x).
−6−5−4−3−2−101234567891011−5−4−3−2−10123456x

Quiz coming up and limits still feel slippery?

Bring your practice questions. We work through them together until every type feels routine.

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  • In person, we meet at the SFU Burnaby campus or in a private meeting room near Brentwood in Burnaby. Online sessions run on Zoom. You choose when you book.