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(a) The curve $ y' = 1/(1 + x^2) $ is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point $ (-1, \frac {1}{2}).

(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

(a) $y=\frac{1}{2} x+1$

(b) Please see the graph of this amazing witch riding on her broom

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it's clear. So a new ranger So we're given why is equal to one over one plus x square. So we need to find the derivative of this and we're gonna use the quotient role, which gives us one plus x square. Comes the derivative of one minus one times the derivative of one plus X square all over one plus x square square. And this gives us negative to X over one plus x square square. No, we plug in to find a slope and we get 1/2 when we substitute the equation for why minus 12. 1/2 is equal to em. Times X plus one we get Why minus one have this equal to 1/2 times X plus one. And this becomes why is equal to when have X plus one. And for part B, we're gonna draw our graph. You don't look like this in our tangent line in red