anonymous
  • anonymous
find the derivative of the function h(x)=sqrt(2-x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
use chain rule
myininaya
  • myininaya
by the sqrt( ) can be written as ( )^(1/2)
anonymous
  • anonymous
we are just in the first section and haven't learned the chain rule, and are required to use a longer method

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myininaya
  • myininaya
ok the definition then
anonymous
  • anonymous
right
myininaya
  • myininaya
\[\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h} =f'(x)\]
myininaya
  • myininaya
where we have f(x)=sqrt(2-x) and so f(x+h)=sqrt(2-(x+h)) <--here just replaced my x's with (x+h)'s
myininaya
  • myininaya
now plug in
myininaya
  • myininaya
sometimes a good method when you are trying to evaluate a limit algebraically and you have a difference/sum of radicals rationalizing might help
myininaya
  • myininaya
to rationalize recall conjugates
myininaya
  • myininaya
for example the conjugate of a-b is a+b and the conjugate of a+b is a-b
myininaya
  • myininaya
do you want to try to see what happens if you do the following: \[\lim_{h \rightarrow 0} \frac{\sqrt{2-(x+h)}-\sqrt{2-x}}{h} \cdot \frac{\sqrt{2-(x+h)}+\sqrt{2-x}}{\sqrt{2-(x+h)}+\sqrt{2-x}}\]
anonymous
  • anonymous
right, I got it down to -1/sqrt2-x-h +sqrt2-x
myininaya
  • myininaya
one sec let me check
myininaya
  • myininaya
that looks pretty sweet
myininaya
  • myininaya
\[\lim_{h \rightarrow 0}\frac{-1}{\sqrt{2-x-h}+\sqrt{2-x}}\]
myininaya
  • myininaya
your job is to just replace h with 0
myininaya
  • myininaya
any you could do a little magic afterwards to make the answer look a bit more tidy
anonymous
  • anonymous
so -1/2sqrt2-x?
anonymous
  • anonymous
thank you!
myininaya
  • myininaya
\[\frac{-1}{2 \sqrt{2-x}} \text{ is \right!} \]

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