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kow [346]
2 years ago
5

Simplify 1/a+b + 1/a-b + 2b/a^2-b^2​

Mathematics
1 answer:
Simora [160]2 years ago
8 0

Answer:

−a^2 b^2 + 2a + 2b

_________________

             a^2

Step-by-step explanation:

<u><em>Please mark as brainliest if answer is right</em></u>  

Have a great day, be safe and healthy  

Thank u  

XD  

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State the restrictions on the range for y=x^4+8x^3+k
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Answer: The range is y \ge k-432

The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.

Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
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x = 0 or x = -6

It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function

y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
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So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value

So that's why the range is y \ge k - 432

Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction. 
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