Question 55 of 90
Q). $\underset{x\to 2}{\lim }\frac{x^2-3x+2}{x-2}$
1.  0
2.  -2/3
3  3
4.  1

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \underset{\mathrm{x}\to 2}{\lim } \frac{{\mathrm{x}}^2-3\mathrm{x}+2}{\mathrm{x}-2} \\ =\underset{\mathrm{x}\to 2}{\lim } \frac{{\mathrm{x}}^2-2\mathrm{x}-\mathrm{x}+2}{\mathrm{x}-2} \\ =\underset{\mathrm{x}\to 2}{\lim } \frac{\mathrm{x}\left(\mathrm{x}-2\right)-1\left(\mathrm{x}-2\right)}{\mathrm{x}-2} \\ =\underset{\mathrm{x}\to 2}{\lim } \frac{\left(\mathrm{x}-1\right)\left(\mathrm{x}-2\right)}{\left(\mathrm{x}-2\right)} \\ =\underset{\mathrm{x}\to 2}{\lim } \left(\mathrm{x}-1\right) \\ =2-1=1 \left[\mathrm{Answer}\right] \end{gathered}$$

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