Let f: R → (0,1) be a continuous function... | Continuity | JEE Advance

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JEE Advance 2017

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Question

Let $f: R \rightarrow(0,1)$ be a continuous function. Then, which of the following functions ( $s$ ) has(have) the value zero at some point in the interval $(0,1)$ ?

Select ALL correct options:

A

$e^x-\int_0^x f(t) \sin t d t$

B

$f(x)+\int_0^{\frac{\pi}{2}} f(t) \sin t d t$

C

$x-\int_0^{\frac{\pi}{2}-x} f(t) \cos t d t$

D

$x^9-f(x)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

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JEE Advance

Mathematics

Easy

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