Local Linear Approximation; Differentials Solutions To Selected ...
Local Linear Approximation; Differentials Solutions To Selected ...
Local Linear Approximation; Differentials Solutions To Selected ...
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4. Find formulas for dy and △y.<br />
(a)<br />
dy<br />
dx<br />
y = x 2 − 2x + 1<br />
= 2x − 2<br />
dy = (2x − 2)dx<br />
△y = f(x + △x) − f(x)<br />
(b) y = sin(x)<br />
dy<br />
dx<br />
= [(x + △x) 2 − 2(x + △x) + 1] − [x 2 − 2x + 1]<br />
= x 2 + 2x △ x + (△x) 2 − 2x − 2 △ x + 1 − x 2 + 2x − 1<br />
= 2x △ x + (△x) 2 − 2 △ x<br />
= cos(x)<br />
dy = cos(x)dx<br />
△y = f(x + △x) − f(x)<br />
= sin(x + △x) − sin(x)<br />
5
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