Question

Let $S$ be a square with sides of length $x$. If we approximate the change in size of the area of $S$ by $h.\frac{dA}{dx}{|}_{x=x_0}$, when the sides are changed from $x_0$ to $x_o+h$, then the absolute value of the error in our approximation, is

• A. $h^2$
• B. $2h{x}_0$
• C. $x_0^2$
• D. $h$

Answer 1

The correct option is A $h^2$

$A=x^2$

$\frac{dA}{dx}=2x$

Given , approximate change in size of area $=\Delta A=h.\frac{dA}{dx}{|}_{x=x_0}$

$\Rightarrow \Delta A=2x_{0}h$

Also, $(A+\Delta A)-A=(x_0+h{)}^2-{x_0}^2$

$=2x_{0}h+h^2$

Hence, absolute value of error in our approximation is $h^2$