laplacetransform cos(t/2)

解答

拉普拉斯变换

cos (\frac{t}{2})

\frac{4 s}{4 s ^{2} + 1}

求解步骤

L {cos (\frac{t}{2})}

使用拉普拉斯变换表:

L {cos (a t)} = \frac{s}{s ^{2} + a ^{2}}

L {cos (\frac{t}{2})} = \frac{s}{s ^{2} + ( \frac{1}{2} ) ^{2}}

= \frac{s}{s ^{2} + ( \frac{1}{2} ) ^{2}}

= \frac{4 s}{4 s ^{2} + 1}

\frac{d}{d x} (ln (\frac{1}{4} e^{x} + \frac{3}{4} e^{- x}))

\frac{d}{d x} (ln ∣ x - 1 ∣)

f^{^{'}} (x) = cos (x), f (0) = - 5

s l o p e in t erce pt (- 10, 3), (- 8, - 8)

n = 0 \sum \infty (\frac{1}{5})^{n + 1}