Let fx=x3+x2−16x+20x−22k If x ≠2 if x = 2, If f(x) is continuous for all x then k =

k=f(2)=Ltx→2 ⁡f(x)=Ltx→2⁡x3+x2−16x+20(x−2)2=Ltx→2⁡3x2+2x−162(x−2)=Ltx→2⁡6x+22=7

Let fx=x3+x2−16x+20x−22k If x ≠2 if x = 2, If f(x) is continuous for all x then k =

k=f(2)=Ltx→2 ⁡f(x)=Ltx→2⁡x3+x2−16x+20(x−2)2=Ltx→2⁡3x2+2x−162(x−2)=Ltx→2⁡6x+22=7

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Let $f (x) = \{\begin{cases} \frac{x^{3} + x^{2} - 16 x + 20}{{(x - 2)}^{2}} \\ k \end{cases} \begin{array}{l} I f x \neq 2 \\ i f x = 2 \end{array},$ If f(x) is continuous for all x then k =

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Detailed Solution

$k = f (2) = \underset{x \to 2}{L t}_{} f (x) = \underset{x \to 2}{L t} \frac{x^{3} + x^{2} - 16 x + 20}{(x - 2)^{2}} = \underset{x \to 2}{L t} \frac{3 x^{2} + 2 x - 16}{2 (x - 2)} = \underset{x \to 2}{L t} \frac{6 x + 2}{2} = 7$

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