Question

PP4 Find approximate value of ( 26.96)1/3​

Answer 1

Answer:

The approximate value of (26.96)^$\frac{1}{3}$ is 2.998096.

Step-by-step explanation:

We know for calculating the approximate value we have to use the following formula,

f(a+x) = f(a) + xf’(a) +  [(x^2)/2 * f’’(a)] + ……

According to the question above  

Let a = 26 and x = 0.96

So, if f(a) = (26)^$\frac{1}{3}$ = 2.962

Then,  

f’(a) = df(a)/dx = 1/3 * (26)^(-2/3) = 0.113 / 3 = 0.0376

Thus,

f(26.96)  

= f(26+0.96)  

= f(26) + [x f’(26)]  

= 2.962 + (0.96 * 0.0376)

= 2.962 + 0.036096

= 2.998096

Hope this helps!!!!!