WBJEE · Maths · Limits
If \(f^{\prime \prime}(0)=k, k \neq 0,\) then the value of \(\lim _{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^{2}}\) is
- A \(k\)
- B \(2 k\)
- C \(3 k\)
- D \(4 k\)
Answer & Solution
Correct Answer
(C) \(3 k\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^{2}}\) \(=\lim _{x \rightarrow 0} \frac{2 f^{\prime}(x)-3 f^{\prime}(2 x) \cdot 2+f^{\prime}(4 x) \cdot 4}{2 x}\) \(=\lim _{x \rightarrow 0} \frac{f^{\prime}(x)-3 f^{\prime}(2 x)+2 f^{\prime}(4 x)}{x}\)…
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