## Thomas' Calculus 13th Edition

a. $y=0$ when $0\leq x\leq \frac{T}{2}$ $y=\frac{2}{T}x-1$ when $\frac{T}{2}\leq x\leq T$ b. $y=A$ when $0\leq x \lt \frac{T}{2}$ $y=-A$ when $\frac{T}{2}\leq x \lt T$ $y=A$ when $T\leq x \lt \frac{3T}{2}$ $y=-A$ when $\frac{3T}{2}\leq x \lt 2T$
a. We can see that the two line segments are: $(0,0)$ to $(\frac{T}{2},0)$ and $(\frac{T}{2},0)$ to $(T,1)$. Using the formula of line equation passing two points: Left line segment: $\frac{y-0}{x-\frac{T}{2}}=\frac{0-0}{0-\frac{T}{2}}$ which gives $y=0$ when $0\leq x\leq \frac{T}{2}$ Right line segment: $\frac{y-1}{x-T}=\frac{0-1}{\frac{T}{2}-T}$ which gives $y=\frac{2}{T}x-1$ when $\frac{T}{2}\leq x\leq T$ b. The four line segments are: $(0,A) to (\frac{T}{2},A)$, $(\frac{T}{2},-A) to (T,A)$, $(T,A) to (\frac{3T}{2},A)$ and $(\frac{3T}{2},-A) to (2T,-A)$ The equations can be easily found as: $y=A$ when $0\leq x \lt \frac{T}{2}$ $y=-A$ when $\frac{T}{2}\leq x \lt T$ $y=A$ when $T\leq x \lt \frac{3T}{2}$ $y=-A$ when $\frac{3T}{2}\leq x \lt 2T$