If y=x^{4}-10 and if x changes from 2 to 1.99 | vedclass

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(A) Given $y = x^{4} - 10$. We need to find the approximate change in $y$ $(\Delta y)$ when $x$ changes from $x = 2$ to $x = 1.99$. Here,$x = 2$ and $

Vedclass · Accepted Answer

-$0.32$

Vedclass · Answer

(A) Given $y = x^{4} - 10$. We need to find the approximate change in $y$ $(\Delta y)$ when $x$ changes from $x = 2$ to $x = 1.99$. Here,$x = 2$ and $\Delta x = 1.99 - 2 = -0.01$. The derivative is $\frac{dy}{dx} = 4x^{3}$. The approximate change is given by $\Delta y \approx \frac{dy}{dx} 	imes \Delta x$. Substituting the values: $\Delta y \approx 4(2)^{3} 	imes (-0.01)$. $\Delta y \approx 4(8) 	imes (-0.01) = 32 	imes (-0.01) = -0.32$. Thus,the change in $y$ is $-0.32$.

If $y=x^{4}-10$ and if $x$ changes from $2$ to $1.99$,what is the change in $y$?

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