Question

find the squar root of follwing 1 to 20

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Answer 1

Answer:

6

Step-by-step explanation:

First of all, x−−√=defx12 .

Now, I’ll represent the square root function by its Taylor series. I’ll calculate this Taylor series about 16 , just to be safe from any annoying radii of convergence. Then, I’ll approximate 20−−√ by setting x=20 in the series.

The definition of the Taylor Series of any anylitic function f(x) is as follows:

f(x)=∑n=0∞f(n)(a)(x−a)nn!

Here, f(n) denotes the n th derivative of f . We will have to calculate lots of derivatives and hopefully there will be a somewhat easily noticeable pattern.

f(x) shall hereafter denote x−−√ .

The “zeroth” derivative of f is simply f . I’ll have f(16) as the coefficient of the first term in the series. (Remember, I decided to center the Taylor Series around 16 . The square root of 16 is easy enough — it’s just 4 . Four fours are 16.)

f(x)=4(x−16)00!+⋯

Okay. Things will be getting a little challenging. We now have to calculate the derivative of x−−√ .

The Power Rule says that ddxxn=nxn−1 . In this case, n=12 (given that x−−√=x12 ).

Therefore, ddxx−−√=12x−12=12x√ . The next

Answer 2

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