Find the value of k such that the function f(x) = (x^2 - 4)/(x - 2) for x is not 2, and f(x) = k for x = 2, is continuous at x = 2.

C. 4 — For continuity at x = 2, the limit of f(x) as x approaches 2 must equal f(2). The limit of (x^2 - 4)/(x - 2) simplifies to the limit of (x + 2), which is 4.

JEE Advanced · MathematicsMedium

$Let f (x) = {\frac{x ^{2} - 4}{x - 2} k x \neq = 2 x = 2 is continuous at x = 2.$

A. $0$
B. $2$
C. $4$
D. $1$

Show correct answer & step-by-step solution

Correct answer: C — $4$

Solution

x \to 2 lim \frac{( x - 2 ) ( x + 2 )}{x - 2} = x \to 2 lim (x + 2) = 4. Thus k = 4.

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Let f(x)={x−2x2−4​k​x=2x=2​ is continuous at x=2.

Solution

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$Let f (x) = {\frac{x ^{2} - 4}{x - 2} k x \neq = 2 x = 2 is continuous at x = 2.$