The Fourier cosine series for an even function f(x) is given by $${\text{f}}\left( {\text{x}} \right) = {{\text{a}}_0} + \sum\limits_{{\text{n}} = 1}^\infty {{{\text{a}}_{\text{n}}}\cos \left( {{\text{nx}}} \right)} $$
The value of the coefficient a2 for the function f(x) = cos2(x) in [0, π] is
A. -0.5
B. 0.0
C. 0.5
D. 1.0
Answer: Option C
A. $$\frac{1}{{{\text{s}} + {\text{a}}}}$$
B. $$\frac{1}{{{\text{s}} - {\text{a}}}}$$
C. $$\frac{1}{{{\text{a}} - {\text{s}}}}$$
D. $$\infty $$
Evaluate $$\int\limits_0^\infty {\frac{{\sin {\text{t}}}}{{\text{t}}}{\text{dt}}} $$
A. $$\pi $$
B. $$\frac{\pi }{2}$$
C. $$\frac{\pi }{4}$$
D. $$\frac{\pi }{8}$$
A. $$\frac{{1 + {{\text{s}}^2}}}{{{{\left( {{{\text{s}}^2} - 1} \right)}^2}}}$$
B. $$\frac{{{\text{st}}}}{{\left( {{{\text{s}}^2} - 1} \right)}}$$
C. $$\frac{{1 - {{\text{s}}^2}}}{{{{\left( {{{\text{s}}^2} - 1} \right)}^2}}}$$
D. $$\frac{{1 + {{\text{s}}^2}}}{{1 - {{\text{s}}^2}}}$$
A. $$\frac{2}{{{\text{s}} + 1}}$$
B. $$\frac{4}{{{\text{s}} + 1}}$$
C. $$\frac{4}{{{{\text{s}}^2} + 1}}$$
D. $$\frac{2}{{{{\text{s}}^2} + 1}}$$
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