Answer:
See below for proof.
Step-by-step explanation:
<u>Given</u>:

<u>First derivative</u>

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<u />
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<u>Second derivative</u>
<u />







<u>Proof</u>



![= \left(x+\sqrt{1+x^2}\right)^m\left[m^2-\dfrac{mx}{\sqrt{1+x^2}}+\dfrac{mx}{\sqrt{1+x^2}}-m^2\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%28x%2B%5Csqrt%7B1%2Bx%5E2%7D%5Cright%29%5Em%5Cleft%5Bm%5E2-%5Cdfrac%7Bmx%7D%7B%5Csqrt%7B1%2Bx%5E2%7D%7D%2B%5Cdfrac%7Bmx%7D%7B%5Csqrt%7B1%2Bx%5E2%7D%7D-m%5E2%5Cright%5D)
![= \left(x+\sqrt{1+x^2}\right)^m\left[0]](https://tex.z-dn.net/?f=%3D%20%5Cleft%28x%2B%5Csqrt%7B1%2Bx%5E2%7D%5Cright%29%5Em%5Cleft%5B0%5D)

Answer: √20 is between 4.47 and 4.48
Step-by-step explanation: Square roots of numbers between perfect squares are irrational numbers. 16 and 25 are squares of 4 and 5, so the irrational number we are looking for must be about halfway between 16 and 25.
is more than 4.47 and less than 4.48
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The lateral area of a cone is equal to

where
r is the radius of the base
l is the slant height
we have


assume 
substitute the values

This value is an underestimate, because the assumed pi value is less than the real value
assumed value 
real value 
Get y by itself so subtract 2x from both sides. So next it would be -4y=-2x+2. To get y by itself divide both sides by -4. So then it would be y= -2/-4x +2/-4. They both reduce down to y=1/2x-1/2. So the slope is 1/2 because the formula y=mx+b
m=slope. Hope this helps! :)