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Let \( f(x) \) be a continuously differentiable function on the interval \( (0, \infty) \) such that \( f(1) = 2 \) and \[ \lim_{t \to x} \frac{t^{10} f(x) - x^{10} f(t)}{t^9 - x^9} = 1 \] for each \( x > 0 \). Then, for all \( x > ...   4 weeks ago admin
iit jee 2024
A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a q   4 weeks ago admin
iit jee probability
Let 𝑓 ( 𝑥 ) f(x) be a continuously differentiable function on the interval ( 0 , ∞ ) (0,∞) such that 𝑓 ( 1 ) = 2 f(1)=2 and lim ⁡ 𝑡 → 𝑥 𝑡 10 𝑓 ( 𝑥 ) − 𝑥 10 𝑓 ( 𝑡 ) 𝑡 9 − 𝑥 9 = 1 t→x lim ​ t 9 −x 9 t 10 f(x)−x 10 f(t) ​ =   4 weeks ago admin
iit jee advanced 2024

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