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  • Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3
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f = (m + n/m)/2 m Example: n=25 Finding the square root of a number

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Page 1: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 2: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 3: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 4: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 5: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 6: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 7: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 8: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 9: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 10: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 11: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 12: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = (m + n/m)/2

mExample: n=25

Finding the square root of a number

Page 13: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 14: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 15: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 16: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 17: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 18: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 19: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

Page 20: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n/m

mExample: n=25

Finding the square root of a number

What is going on?

Page 21: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 22: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 23: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 24: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 25: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 26: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 27: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 28: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 29: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f (n,m)

m

Finding the square root of a number

What is going on?

Page 30: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 31: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 32: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 33: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 34: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 35: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 36: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 37: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 38: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 39: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 40: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - m/2

m

Finding the square root of a number

What is going on?

Example: n=15 from m=2n/3

Page 41: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - 2m

m

Finding the square root of a number

Example: n=30 from m=n/3

Try a line of slope of magnitude greater than 1

Page 42: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - 2m

m

Finding the square root of a number

Example: n=30 from m=n/3

Page 43: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - 2m

m

Finding the square root of a number

Example: n=30 from m=n/3

Page 44: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - 2m

m

Finding the square root of a number

Example: n=30 from m=n/3

Page 45: Finding the square root of a number f = (m + n/m)/2gauss.ececs.uc.edu/Courses/c110/lectures/Week1/sqrt.pdff = n - 2m m Finding the square root of a number Example: n=30 from m=n/3

f = n - 2m

m

Finding the square root of a number

Example: n=30 from m=n/3


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