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INSTRUCTORS Raffi Hovasapian John Zhu
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Lecture Comments (8)

0 answers

Post by Rohit Kumar on October 10 at 04:31:22 PM

How can you get 1/0 to equal infinity right away. How would you proceed with the indeterminate form?

0 answers

Post by Zhe Tian on September 2, 2015

why would 1/0 = infinity???

1 answer

Last reply by: Javier Anton
Thu Nov 28, 2013 12:50 AM

Post by Javier Anton on November 28, 2013

I believe dividing any real number by zero is undefined not infinity. The real answer should not be infinity.

0 answers

Post by Erika O on February 28, 2013

why does it become 0 at infinity?

0 answers

Post by Narin gopaul on September 10, 2012

in question 1 why did you divide everything by x ?

1 answer

Last reply by: Harpreet Singh
Sat Mar 23, 2013 10:33 AM

Post by Ivan Murray on June 5, 2012

I think on example #4, you're supposed to divide by X^2 not X^4. Then the answer comes out to infinity. The answer John obtained, 1/0, would be undefined.

Solving Limits with Algebra

  • Simplify until we can plug-in x without reaching an undefined value
    • Method 1: Divide all terms by highest degree polynomial term
    • Method 2: “unfoil”, then cancel terms in numerator and denominator

Solving Limits with Algebra

Find limx → ∞ x
  • As x approaches infinity, limx → ∞ x goes to infinity.
limx → ∞ x = ∞
Find limx → ∞ [1/x]
  • Dividing a finite number by an infinitely large number will always result in zero.
limx → ∞ [1/x] = 0
Find limx → ∞ (x + [1/x])
  • limx → ∞ (x + [1/x]) = limx → ∞ x + limx → ∞ [1/x] = ∞+ 0 = ∞
Find limx → ∞ [(3x2)/(x2)]
  • Divide by the largest exponent
  • limx → ∞ [(3x2)/(x2)] = limx → ∞ [([(3x2)/(x2)])/([(x2)/(x2)])] = limx → ∞ [3/1] = 3
3
Find limx → ∞ [3x/(x + 5)]
  • limx → ∞ [3x/(x + 5)] = limx → ∞ [([3x/x])/([(x + 5)/x])]
    = limx → ∞ [3/(1 + [5/x])]
    = [3/(1 + 0)] = 3
3
Find limx → ∞ [(x + 5)/3x]
  • limx → ∞ [(x + 5)/3x] = limx → ∞ [([(x + 5)/x])/([3x/x])]
    = limx → ∞ [(1 + [5/x])/3]
    = [(1 + 0)/3]
    = [1/3]
[1/3]
Find limx → ∞ [(x − 4)/(x2 + 2)]
  • limx → ∞ [(x − 4)/(x2 + 2)] = limx → ∞ [([(x − 4)/(x2)])/([(x2 + 2)/(x2)])]
    = limx → ∞ [([1/x] − [4/(x2)])/(1 + [2/(x2)])]
    = [(0 − 0)/(1 + 0)]
    = [0/1]
    = 0
0
Find limx → ∞ [(x2 + 500)/(x2 − 25)]
  • limx → ∞ [(x2 + 500)/(x2 − 25)] = limx → ∞ [([(x2 + 500)/(x2)])/([(x2 − 25)/(x2)])]
    = limx → ∞ [(1 + [500/(x2)])/(1 − [25/(x2)])]
    = [(1 + 0)/(1 − 0)] = 1
1
Find limx → ∞ [(2x3 − 3x2 + 5x + 7)/(11x3 + 13)]
  • limx → ∞ [(2x3 − 3x2 + 5x + 7)/(11x3 + 13)] = limx → ∞[([(2x3 − 3x2 + 5x + 7)/(x3)])/([(11x3 + 13)/(x3)])]
    = limx → ∞ [(2 − [3/x] + [5/(x2)] + [7/(x3)])/(11 + [13/(x3)])]
    = [(2 − 0 + 0 + 0)/(11 + 0)]
    = [2/11]
[2/11]
Find limx → ∞ [(12x4 + 5x)/(x3)]
  • limx → ∞ [(12x4 + 5x)/(x3)] = limx → ∞ [([(12x4 + 5x)/(x4)])/([(x3)/(x4)])]
    = limx → ∞ [(12 + [5/(x3)])/([1/x])]
    = limx → ∞ (12x + [5/(x2)])
    = ∞+ 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

Solving Limits with Algebra

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
  • Solving Limits with Algebra 0:07
    • Example 1: Solve Algebraically
  • Solving Limits with Algebra, Example 2 2:28
  • Solving Limits with Algebra, Example 3 3:18
  • Solving Limits with Algebra, Example 4 4:56
  • Solving Limits with Algebra, Example 5 6:26