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  • If y = x^4 -10 and if x changes from 2 to 1.99, what is the change in y A. 0.32

If y = x^4 - 10and if x changes from 2 to 1.99, what is the change in y
A. 0.32

B. 0.032
C. 5.68
D. 5.968

Answers (1)

A)

Given y = x^4 - 10

Differentiate on both sides with x and get

\frac{\mathrm{d}(\mathrm{y})}{\mathrm{dx}}=\frac{\mathrm{d}\left(\mathrm{x}^{4}-10\right)}{\mathrm{dx}}

Apply power rule and get
\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=4 \mathrm{x}^{3}
Now, value of x changes from 2 to 1.99, so the change in x is
\Delta x=2-1.99=0.01
So the change in y is,
\Rightarrow \Delta y=\frac{d y}{d x} \times \Delta x

Substitute corresponding values and get

\Rightarrow \Delta y=4x\textsuperscript{3} \times (0.01)

Now at x=2, the change in y becomes

\\ { \Rightarrow \Delta y\textsubscript{x=2}=4(2)\textsuperscript{3} \times (0.01)}\\ { \Rightarrow \Delta y\textsubscript{x=2}=4 \times 8 \times (0.01)}\\ { \Rightarrow \Delta y\textsubscript{x=2}=0.32}\\

Therefore, change in y is 0.32.

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infoexpert22

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