Question:medium
If $f''(0) = k$, then $\displaystyle\lim_{x\to 0} \dfrac{2f(x) - 3f(2x) + f(4x)}{x^{2}}$ equals
If $f''(0) = k$, then $\displaystyle\lim_{x\to 0} \dfrac{2f(x) - 3f(2x) + f(4x)}{x^{2}}$ equals
Show Hint
For limits of the form $[2f(x)-3f(2x)+f(4x)]/x^2$, expand via Taylor series — the $f(0)$ and $f'(0)$ terms cancel, and only the $f''(0)$ term contributes.
Updated On: Apr 8, 2026
- $k$
- $2k$
- $3k$
- $4k$
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The Correct Option is C
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