If the function $$f(x)=\begin{cases} \frac{2}{x} \left\{ \sin(k_1 + 1)x + \sin(k_2 -1)x \right\}, & x 0 \end{cases}$$ is continuous at $$x = 0$$, then $$k_1^2 + k_2^2$$ is equal to:

If the function f(x)= 2/x { sin(k₁ + 1)x + sin(k₂ -1)x }, x < 0 4… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 23 January, Shift 1Continuity

If the function $f(x)=\begin{cases} \frac{2}{x} \left\{ \sin(k_1 + 1)x + \sin(k_2 -1)x \right\}, & x < 0\\ 4, & x = 0\\ \frac{2}{x} \log_e \left( \frac{2 + k_1 x}{2 + k_2 x} \right), & x > 0 \end{cases}$ is continuous at $x = 0$ , then $k_1^2 + k_2^2$ is equal to:

A
$8$
B
$20$
C
$5$
D
$10$

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