If f(x) = x2 , find the value of \(\frac{(f)(1.1)-f(1)}{(1.1)-1}\)

1.	If f(x) = x2 , find the value of \(\frac{(f)(1.1)-f(1)}{(1.1)-1}\)
Answer» Given: f(x) = x² Firstly, we find the f(1.1) Putting the value of x = 1.1 in the given eq., we get f(1.1) = (1.1)² ⇒ f(1.1) = 1.21 Similarly, f(1) = (1)² ⇒ f(1) = 1 Putting the value of f(1.1) and f(1) in eq. (i), we get \(\frac{f(1.1)-f(1)}{(1.1-1)}\) = \(\frac{1.21-1}{1.1-1}\) = \(\frac{0.21}{0.1}\) = 2.1 Hence, the value of \(\frac{f(1.1)-f(1)}{(1.1-1)}\) = 2.1

Answer»

Given: f(x) = x²

Firstly, we find the f(1.1)

Putting the value of x = 1.1 in the given eq., we get

f(1.1) = (1.1)²

⇒ f(1.1) = 1.21

Similarly,

f(1) = (1)²

⇒ f(1) = 1

Putting the value of f(1.1) and f(1) in eq. (i), we get

\(\frac{f(1.1)-f(1)}{(1.1-1)}\) = \(\frac{1.21-1}{1.1-1}\) = \(\frac{0.21}{0.1}\) = 2.1

Hence, the value of \(\frac{f(1.1)-f(1)}{(1.1-1)}\) = 2.1

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