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INSTRUCTORS Raffi Hovasapian John Zhu
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For more information, please see full course syllabus of Calculus AB
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Lecture Comments (2)

0 answers

Post by Jessica Lee on August 30, 2014

On second to last example, how do we know if lim x-> infinity 1^2/x^n=0? I thought the property says k/x^n=0?

0 answers

Post by Erika O on February 21, 2013

Great video. I have been having a lot of trouble grasping what exactly a limit is. This video completely.

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Limit Definition & Properties

  • Value of y or f(x) as x approaches some number

Limit Definition & Properties

Find limx → 2 x
  • Let's see how the function behaves as we get close to x = 2
  • f(1.9) = 1.9
  • f(1.99) = 1.99
  • f(2.01) = 2.01
  • f(2.1) = 2.1
limx → 2 x = 2
Find limx → 0 π
  • This is a constant function, so no matter what value we input, the same constant is returned.
limx → 0 π = π
Given f(x) = [1/(|x|)], find f(0)
f(0) = [1/0] = undefined
Find limx → 0 [1/(|x|)]
  • f(−.1) = 10
  • f(−.01) = 100
  • f(−.0001) = 10000
  • f(.0001) = 10000
  • f(.01) = 100
limx → 0 [1/(|x|)] = ∞
If the limx → 1 f(x) = 3 and limx → 1 g(x) = 4, find limx → 1 f(x) + g(x)
  • limx → 1 f(x) + g(x) = limx → 1 f(x) + limx → 1 g(x) = 3 + 4 = 7
7
Using the values from the previous problem, find limx → 1 f(x)g(x)
  • limx → 1 f(x)g(x) = limx → 1 f(x) * limx → 1 g(x) = 3 * 4 = 12
12
If limx → 0 f(x) = 2, find limx → 0 5f(x)
  • limx → 0 5f(x) = 5limx → 0 f(x) = 5 * 2 = 10
10
If limx → 0 f(x) = 2, find limx → 0 (3 + f(x))
  • limx → 0 (3 + f(x)) = 3 + limx → 0 f(x) = 3 + 2 = 5
5
Find limx → 0 sin(x)ex given limx → 0 sin(x) = 0 and limx → 0 ex = 1
  • limx → 0 sin(x)ex = limx → 0 sin(x) * limx → 0 ex = 0 * 1 = 0
0
Find limx → ∞ [(√x)/x]
  • limx → ∞ [(√x)/x] = limx → ∞ [1/(√x)]
  • The square root in the denominator doesn't matter much here, we're still dividing a constant by an infinitely large number
limx → ∞ [1/(√x)] = 0

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Limit Definition & Properties

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Definition 0:06
    • Example: Limit
  • Properties 1:13
    • 1st Property
    • 2nd Property
    • Special Property
  • Limits 2:36
    • Explain Example
  • Limits Example 4:39
  • Limits Example 5:21