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Bio has helped students
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Summary of contribution activity by day
Longest streak: 115 days
232 thank you notes
Someone from Detroit, United States
On my exam, thank you
for this
answer
1 week ago
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Someone from Bryn Mawr, United States
Thank you
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1 week ago
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Someone from United States
just what i needed
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2 weeks ago
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Bio
Bio joined Socratic 2 years ago. Bio hasn't written a biography yet.
205K karma · Singapore
Activity
750 Answers
366 Edits
1 Asked
@bio
Bio
updated
the answer to
Why are convex mirrors used instead of concave mirrors as rear view mirrors?
.
2 months ago
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@bio
Bio
updated
the answer to
Which gas turns lime to water milky? (Oxygen/Carbon dioxide)
.
3 months ago
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Nicki liked this.
@bio
Bio
wrote an answer to
How do you solve #abs(8-2n)=2#?
.
3 months ago
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@bio
Bio
wrote an answer to
How do you find the average value of the function for #f(x)=2-1/2x, 0<=x<=4#?
.
3 months ago
·
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@bio
Bio
commented
@Slithern
You are right
on
How do you solve #2sin^2x-cosx=1# on the interval [0,2pi]?
3 months ago
·
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@bio
Bio
wrote an answer to
How do you find the points of intersection of #theta=pi/4, r=2#?
.
4 months ago
·
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@bio
Bio
commented
If the inverse of #f'(x)# exists, then you will get
#x = f^(-1)(y)#
or
#y = f(x)#
on
Can someone explain why this happens?
4 months ago
·
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@bio
Bio
commented
Therefore, the Above Equation simplifies to
#f'(x) = 1/{d/{dy}(f^(-1)(y))} = f'(f^(-1)(y))#
or to write it more clearly
#f'(x) = f'(f^(-1)(y))#
on
Can someone explain why this happens?
4 months ago
·
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@bio
Bio
commented
However, as mentioned by Jim, the right side can be simplified. In particular,
#d/{dy}(f^(-1)(y))#
#= d/{dy}(x)#
#= 1/({dy}/{dx})#
#= 1 / ( f'(x) )#
#= 1 / ( f'( f^(-1)(y) ) )#
on
Can someone explain why this happens?
4 months ago
·
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@bio
Bio
commented
The reason is because for the Above Equation to hold, #y=f(x)# is a pre-requisite, In other words,
#y = f(x) implies f'(x) = 1/{d/{dy}(f^(-1)(y))}#
but not the other way round.
on
Can someone explain why this happens?
4 months ago
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