Choose the correct answer from the given four options: If y=x^4-1… - Vidyadip

MCQ

Choose the correct answer from the given four options: If $y=x^4-10$ and if $x$ changes from $2$ to $1.99,$ what is the change in $y:$

A
$0.32$
B
$0.03.2$
C
$5.68$
✓
$5.968$

✓

Answer

Correct option: D.

$5.968$

We have, $y=x^4-10$
$\Rightarrow\ \frac{\text{dy}}{\text{dx}}=4\text{x}^3$
and $\triangle\text{x}=2.00-1.99=0.01$
$\therefore\ \triangle\text{y}=\frac{\text{dy}}{\text{dx}}\times\triangle\text{x}$
$=4\text{x}^3\times\triangle\text{x}$
$=4\times2^3\times0.01$
$=32\times0.01=0.32$
So, the approximate change in $y$ is $0.32.$

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