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Find the slope of the tangent to the curve \(\normalsize y =\large { \frac{x-1}{x-2},} \normalsize x \neq 2\; at\;x = 10\)

$\begin{array}{1 1} (A)\;\large\frac{1}{64} \\ (B)\;\large\frac{-1}{64} \\ (C)\; 64 \\ (D)\;-64 \end{array} $

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  • If $y=f(x)$ then $\large\frac{dy}{dx}$=slope of the tangent to $y=f(x)$ at point $P$.
Step 1:
Differentiating w.r.t $x$ on both sides,by applying the quotient rule,
Step 2:
$\large\frac{dy}{dx}$ at $x=10$
Substituting for $x$ we get,
Hence the slope of the tangent to the curve $y=\large\frac{x-1}{x-2}$ is $\large\frac{-1}{64}$
answered Jul 10, 2013 by sreemathi.v

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