24 lines
500 B
TeX
24 lines
500 B
TeX
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\beginsection 28.2
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Use the {\it definition} of derivative to calculate the derivatives of the
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following functions at the indicated points.
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\medskip
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(a) $f(x)=x^3$ at $x=2$
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\medskip
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$$\eqalign{
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f^\prime&=\lim_{x\rightarrow2}{f(x)-f(2)\over x-2}\cr
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&=\lim_{x\rightarrow2}{x^3-8\over x-2}\cr
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&=\lim_{x\rightarrow2}x^2+2x+4\cr
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&=12
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}$$
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\medskip
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(b) $g(x)=x+2$ at $x=a$
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\medskip
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$$\eqalign{
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g^\prime(a)&=\lim_{x\rightarrow a}{g(x)-g(a)\over x-a}\cr
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&=\lim_{x\rightarrow a}{x+2-a-2\over x-a}\cr
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&=1
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}$$
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