Mixing
For the function 𝑓(𝑥)=(16/𝑥^2), simplify each expression as much as possible.
$begingroup$
For the function 𝑓(𝑥)=(16/𝑥^2), simplify each expression as much as possible.
- (𝑓(𝑥+ℎ)−𝑓(𝑥))/ℎ, ℎ≠0:
- (𝑓(𝑤)−𝑓(𝑥))/𝑤−𝑥, 𝑥≠𝑤:
algebra-precalculus
asked Jan 19 at 22:35
mfmmfm
11
$endgroup$
add a comment |
$begingroup$
For the function 𝑓(𝑥)=(16/𝑥^2), simplify each expression as much as possible.
- (𝑓(𝑥+ℎ)−𝑓(𝑥))/ℎ, ℎ≠0:
- (𝑓(𝑤)−𝑓(𝑥))/𝑤−𝑥, 𝑥≠𝑤:
algebra-precalculus
asked Jan 19 at 22:35
mfmmfm
11
$endgroup$
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37
add a comment |
$begingroup$
For the function 𝑓(𝑥)=(16/𝑥^2), simplify each expression as much as possible.
- (𝑓(𝑥+ℎ)−𝑓(𝑥))/ℎ, ℎ≠0:
- (𝑓(𝑤)−𝑓(𝑥))/𝑤−𝑥, 𝑥≠𝑤:
algebra-precalculus
asked Jan 19 at 22:35
mfmmfm
11
$endgroup$
For the function 𝑓(𝑥)=(16/𝑥^2), simplify each expression as much as possible.
- (𝑓(𝑥+ℎ)−𝑓(𝑥))/ℎ, ℎ≠0:
- (𝑓(𝑤)−𝑓(𝑥))/𝑤−𝑥, 𝑥≠𝑤:
algebra-precalculus
algebra-precalculus
asked Jan 19 at 22:35
mfmmfm
11
asked Jan 19 at 22:35
mfmmfm
11
asked Jan 19 at 22:35
mfmmfm
11
asked Jan 19 at 22:35
mfmmfm
11
asked Jan 19 at 22:35
mfmmfm
11
11
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37
add a comment |
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37
add a comment |
1 Answer
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$begingroup$
$$frac{f(x+h)-f(x)}{h}=frac{frac{16}{(x+h)^2}-frac{16}{x^2}}{h}=frac{frac{16[x^2-(x+h)^2]}{x^2(x+h)^2}}{h}=frac{16(x-x-h)(x+x+h)}{hx^2(x+h)^2}=frac{16h(2x+h)}{hx^2(x+h)^2}=frac{16(2x+h)}{x^2(x+h)^2}=frac{16}{x(x+h)^2}+frac{16}{x^2(x+h)}$$
$$frac{f(w)-f(x)}{w-x}=frac{frac{16}{w^2}-frac{16}{x^2}}{w-x}=frac{16(x^2-w^2)}{w^2x^2(w-x)}=-frac{16(w+x)}{w^2x^2}$$
answered Jan 19 at 22:46
user289143user289143
1,002313
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
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active
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$begingroup$
$$frac{f(x+h)-f(x)}{h}=frac{frac{16}{(x+h)^2}-frac{16}{x^2}}{h}=frac{frac{16[x^2-(x+h)^2]}{x^2(x+h)^2}}{h}=frac{16(x-x-h)(x+x+h)}{hx^2(x+h)^2}=frac{16h(2x+h)}{hx^2(x+h)^2}=frac{16(2x+h)}{x^2(x+h)^2}=frac{16}{x(x+h)^2}+frac{16}{x^2(x+h)}$$
$$frac{f(w)-f(x)}{w-x}=frac{frac{16}{w^2}-frac{16}{x^2}}{w-x}=frac{16(x^2-w^2)}{w^2x^2(w-x)}=-frac{16(w+x)}{w^2x^2}$$
answered Jan 19 at 22:46
user289143user289143
1,002313
$endgroup$
add a comment |
$begingroup$
$$frac{f(x+h)-f(x)}{h}=frac{frac{16}{(x+h)^2}-frac{16}{x^2}}{h}=frac{frac{16[x^2-(x+h)^2]}{x^2(x+h)^2}}{h}=frac{16(x-x-h)(x+x+h)}{hx^2(x+h)^2}=frac{16h(2x+h)}{hx^2(x+h)^2}=frac{16(2x+h)}{x^2(x+h)^2}=frac{16}{x(x+h)^2}+frac{16}{x^2(x+h)}$$
$$frac{f(w)-f(x)}{w-x}=frac{frac{16}{w^2}-frac{16}{x^2}}{w-x}=frac{16(x^2-w^2)}{w^2x^2(w-x)}=-frac{16(w+x)}{w^2x^2}$$
answered Jan 19 at 22:46
user289143user289143
1,002313
$endgroup$
add a comment |
$begingroup$
$$frac{f(x+h)-f(x)}{h}=frac{frac{16}{(x+h)^2}-frac{16}{x^2}}{h}=frac{frac{16[x^2-(x+h)^2]}{x^2(x+h)^2}}{h}=frac{16(x-x-h)(x+x+h)}{hx^2(x+h)^2}=frac{16h(2x+h)}{hx^2(x+h)^2}=frac{16(2x+h)}{x^2(x+h)^2}=frac{16}{x(x+h)^2}+frac{16}{x^2(x+h)}$$
$$frac{f(w)-f(x)}{w-x}=frac{frac{16}{w^2}-frac{16}{x^2}}{w-x}=frac{16(x^2-w^2)}{w^2x^2(w-x)}=-frac{16(w+x)}{w^2x^2}$$
answered Jan 19 at 22:46
user289143user289143
1,002313
$endgroup$
$$frac{f(x+h)-f(x)}{h}=frac{frac{16}{(x+h)^2}-frac{16}{x^2}}{h}=frac{frac{16[x^2-(x+h)^2]}{x^2(x+h)^2}}{h}=frac{16(x-x-h)(x+x+h)}{hx^2(x+h)^2}=frac{16h(2x+h)}{hx^2(x+h)^2}=frac{16(2x+h)}{x^2(x+h)^2}=frac{16}{x(x+h)^2}+frac{16}{x^2(x+h)}$$
$$frac{f(w)-f(x)}{w-x}=frac{frac{16}{w^2}-frac{16}{x^2}}{w-x}=frac{16(x^2-w^2)}{w^2x^2(w-x)}=-frac{16(w+x)}{w^2x^2}$$
answered Jan 19 at 22:46
user289143user289143
1,002313
answered Jan 19 at 22:46
user289143user289143
1,002313
answered Jan 19 at 22:46
user289143user289143
1,002313
answered Jan 19 at 22:46
user289143user289143
1,002313
1,002313
add a comment |
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$begingroup$
Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Jan 19 at 22:59
$begingroup$
What don't you understand? just write all the $f(stuff)$ ans $frac {16}{stuff^2}$ and then do all the math to simplify. It's ... work. But it's straight forwards and unless you tell us where you have problems there's no reason you shouldn't be able to do it.
$endgroup$
– fleablood
Jan 20 at 0:37