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[a]

[tex] \vec{r(t)} <e^tcost, e^tsint> [/tex]

**Give a parametric equation for the line tangent to this curve at**[itex]t = \frac{pi}{4}.[/itex][tex] \vec{r(t)} <e^tcost, e^tsint> [/tex]

[tex]\vec{r(\frac{pi}{4})} = <e^\frac{pi}{4}cos\frac{pi}{4}, e^\frac{pi}{4}sin\frac{pi}{4}[/tex]

[tex] = e^\frac{pi}{4}<\frac{1}{2}, \frac{1}{2}>[/tex]

[tex] \vec {r'(t)} = e^t<cost - sint, cost + sint>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<cos\frac{pi}{4} - sin\frac{pi}{4}, cos\frac{pi}{4} + sin\frac{pi}{4}>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<0,1>[/tex]

[tex] x = \frac{e^\frac{pi}{4}}{2} [/tex]

[tex] y = \frac{e^\frac{pi}{4}}{2} + e^\frac{pi}{4}t [/tex]

My answers aren't right. I suck.

Couldn't even solve for**Give the equation for this same tangent line in the form**[tex]ax + by = c[/tex]**My attempt**[tex]\vec{r(\frac{pi}{4})} = <e^\frac{pi}{4}cos\frac{pi}{4}, e^\frac{pi}{4}sin\frac{pi}{4}[/tex]

[tex] = e^\frac{pi}{4}<\frac{1}{2}, \frac{1}{2}>[/tex]

[tex] \vec {r'(t)} = e^t<cost - sint, cost + sint>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<cos\frac{pi}{4} - sin\frac{pi}{4}, cos\frac{pi}{4} + sin\frac{pi}{4}>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<0,1>[/tex]

[tex] x = \frac{e^\frac{pi}{4}}{2} [/tex]

[tex] y = \frac{e^\frac{pi}{4}}{2} + e^\frac{pi}{4}t [/tex]

My answers aren't right. I suck.

Couldn't even solve for

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