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Limits Continuity and Differentiability question

2025 · 4 Apr · Shift 1 · Q26

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 4 Apr · Shift 1 · Q26

Limits Continuity and Differentiability question

2025 · 4 Apr · Shift 1 · Q26

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f: \mathbb{R} \rightarrow \mathbb{R}

be a continuous function satisfying

f(0)=1

and

f(2 x)-f(x)=x

for all

x \in \mathbb{R}

. If

\lim_{n \rightarrow \infty}\left\{f(x)-f\left(\frac{x}{2^n}\right)\right\}=G(x)

, then

\sum_{r=1}^{10} G\left(r^2\right)

is equal to

A
215
B
420
C
385
D
540

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