Question

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

• A. $e^x-{\int }_0^{1}f\left(t\right)\sin tdt$
• B. $f\left(x\right)+{\int }_0^{1}f\left(t\right)\sin tdt$
• C. $x-{\int }_0^{\frac{\pi }{2}-x}f\left(t\right)\cos tdt$
• D. $x^3-f\left(x\right)$

Answer 1

Answer: (C), (D)

The correct options are
C $x-{\int }_0^{\frac{\pi }{2}-x}f\left(t\right)\cos tdt$
D $x^3-f\left(x\right)$