When adding fractions, we usually find the least common denominator and rewrite both fractions with that denominator. But do you really need the least common denominator? In the sum 3 8 + 5 12 , first add by using the least common denominator. Then add by using a common denominator that is the product of the two original denominators. Do you get the same answer? Try again for the sum 5 6 + 5 9 . What can you conclude? What is the advantage of finding the least common denominator?
When adding fractions, we usually find the least common denominator and rewrite both fractions with that denominator. But do you really need the least common denominator? In the sum 3 8 + 5 12 , first add by using the least common denominator. Then add by using a common denominator that is the product of the two original denominators. Do you get the same answer? Try again for the sum 5 6 + 5 9 . What can you conclude? What is the advantage of finding the least common denominator?
Solution Summary: The author explains the advantage of finding least common denominator by solving the given tions using L.C.D.
When adding fractions, we usually find the least common denominator and rewrite both fractions with that denominator. But do you really need the least common denominator? In the sum
3
8
+
5
12
,
first add by using the least common denominator. Then add by using a common denominator that is the product of the two original denominators. Do you get the same answer? Try again for the sum
5
6
+
5
9
.
What can you conclude? What is the advantage of finding the least common denominator?
A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
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Understanding Fractions, Improper Fractions, and Mixed Numbers; Author: Professor Dave Explains;https://www.youtube.com/watch?v=qyW2mWvvtZ8;License: Standard YouTube License, CC-BY