Question

calculate the approximate value of √10 to four decimal places by application of tailors series​

Answer 1

Answer:

Taylor series approximation uses a Taylor series to represent a number as a polynomial that has a very similar value to the number in a neighborhood around a specified xx value:

f(x) = f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots.

f(x)=f(a)+

1!

f

′

(a)

(x−a)+

2!

f

′′

(a)

(x−a

Answer 2

Answer:

The square root of 10 correct to four places of decimal is 3. 1623.

Step-by-step explanation:

From the above question,

They have given :

The approximate value of √10 to four decimal places by application of tailors series​.

Taylor series is given as

$f(a+h)=f(a)+h.f'(a)+{h^2\over 2!}f''(a)+{h^3\over 3!}f'''(a)+...f(a+h)$

10=9+1

Now, let's have a function that will enable us use Taylor series method

$f(10)=f(9+1)f(10)=f(9+1)$

$a=9a=9 and h=1h=1$

Since we are asked to find the square root

f(a)=a21⟹f(a+1)=10

f(a)=a21⟹f(a+1)=10

Substituting the value of aa we have

$f(a)=9^{1\over 2} =3f(a)=921=3$

$f′(a)=21a21−1=21a−21=a2121=2a211$

f(10)=f(9+1)f(10)=f(9+1)

$\sqrt{10}=5.10471 10​ =5.10471\sqrt{10}=5.10471 10​ =5.10471\sqrt{10}=5.1047 10​ =5.1047\sqrt{10}=5.1047 10​ =5.1047 correct to four decimal places$

To calculate the approximate value of √10 to four decimal places by application of tailors series​,

For a smooth function, the Taylor polynomial is the truncation at the order k of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation.

$\sqrt{10}$  = 5.1047

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