If the function fx-x2-A-2x-Ax-2 for x- 2 2 for x - 2- iscontinuous at x - 2 - then

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Derivative of Standard Functions

If the functi...

Question

If the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{x^{2} - (A + 2) x + A}{x - 2} & f o r x \neq 2 2 & f o r x = 2 \end{matrix}$ is
continuous at $x = 2$ , then

A = 0

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A = 1

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A = - 1

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A = 2

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Solution

The correct option is A $A = 0$
Since, the denominator goes to $0$ as $x$ approaches $2$
The function should be of $\frac{0}{0}$ form
Hence as $x$ goes to $2, x^{2} - (A + 2) x + A$ goes to $0$
$= 4 - 2 (A + 2) + A = 0$
$\Rightarrow A = 0$

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If the function f(x)=⎧⎪⎨⎪⎩x2−(A+2)x+Ax−2for x≠22for x=2 iscontinuous at x=2 , then

The correct option is A A=0Since, the denominator goes to 0 as x approaches 2The function should be of 00 formHence as x goes to 2,x2−(A+2)x+A goes to 0=4−2(A+2)+A=0⇒A=0

If the function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{x^{2} - (A + 2) x + A}{x - 2} & f o r x \neq 2 2 & f o r x = 2 \end{matrix}$ is
continuous at $x = 2$ , then

The correct option is A $A = 0$
Since, the denominator goes to $0$ as $x$ approaches $2$
The function should be of $\frac{0}{0}$ form
Hence as $x$ goes to $2, x^{2} - (A + 2) x + A$ goes to $0$
$= 4 - 2 (A + 2) + A = 0$
$\Rightarrow A = 0$