Manipal Entrance Test 2020 Math Paper

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Question : 11 of 70

Marks: +1, -0

Let f(x) be differentiable on the interval (0,∞) such that f(1)=1 and

lim

t→x

‌

t2f(x)−x2f(t)

t−x

=1 for each x>0. Then, f(x) is equal to

‌
1
3x
+‌
2
3
x2
−‌
x
3
+‌
4x2
3
−‌
1
x
−‌
1
x
+‌
2
x2

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