Question

Can someone double-check my answer? Finding the equation of the tangent of a curve?

Answer 1

this must be a long problem!

Answer 2

equation of tangent line at point (x1,y1)
\[y = f'(x_1) (x - x_1) + y_1\]

Answer 3

\[x=t-t ^{-1}, y=1+t ^{2}; t=1\]\[\frac{ dx }{ dt }=1+t ^{-2}, \frac{ dy }{ dt }=2t\]When t=1, \[x_{1}=1-1^{-1}=0\]\[y_{1}=1+1^{2}=2\]\[\frac{ dy }{ dx }=\frac{ 2t }{ 1+t ^{-2} }=\frac{ 2 }{ 2 }=1\]
\[y-2=1(x-0)\]\[y=x+2\]

Answer 4

It's a simple problem, but I just want to make sure I have the steps right :)

Answer 5

looks good to me

Answer 6

i concur

Answer 7

mmmm \(\pi\)

Answer 8

haha :)