Question

In the Fourier series expansion of
f(x) = 1, -1<x< 0
= cos (7x), 0<x< 1
and period 2 then Fourier coefficient a0 is
​

Answer 1

Answer:

- 7 < 4x + 1 < 23 where x ∈ I

Here the given inequality is

EVALUATION

\sf{ - 7 < 4x + 1 < 23}

Now I is the set of integers

Now we solve the inequality

\sf{ - 7 < 4x + 1 < 23}

\implies \: \sf{ - 7 - 1< 4x + 1 - 1 < 23 - 1}

\implies \: \sf{ - 8 \: < 4x < 22}

\displaystyle \implies \: \sf{ - \frac{8}{4} \: < \frac{4x}{4} < \frac{22}{4} }

\displaystyle \implies \: \sf{ - 2 \: < x < \frac{11}{2} }

\displaystyle \implies \: \sf{ - 2 \: < x < 5.5 }

Since x is an integer