Question:medium
Let \(f\) be a differentiable function satisfying
\[
f(x+y)=f(x)+f(y)-xy \quad \text{for all } x,y\in\mathbb{R}.
\]
If
\[
\lim_{h\to 0}\frac{f(h)}{h}=3,
\]
then the value of
\[
\sum_{n=1}^{10} f(n)
\]
is equal to:
Let \(f\) be a differentiable function satisfying
\[
f(x+y)=f(x)+f(y)-xy \quad \text{for all } x,y\in\mathbb{R}.
\]
If
\[
\lim_{h\to 0}\frac{f(h)}{h}=3,
\]
then the value of
\[
\sum_{n=1}^{10} f(n)
\]
is equal to:
Show Hint
Functional equations involving \(f(x+y)\) often lead to polynomial solutions.
Always use the given limit to fix remaining constants.
Updated On: Mar 5, 2026
- \(-\dfrac{55}{2}\)
- \(\dfrac{275}{2}\)
- \(-\dfrac{55}{4}\)
- \(\dfrac{225}{4}\)
Show Solution
The Correct Option is A
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