- #1

karush

Gold Member

MHB

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The graph of $y=e^{\tan x}-2$ crosses the x-axis at one point in the interval [0,1]

What is the

*of the graph at this point.*

**slope**a, 0.606 b. 2 c, 2.242 d.2.961 e.3.747

[d]

$\begin{array}{rll}

\textit{given} &e^{\tan \:x}-2 &(1)\\

\textit{rewrite} &e^{\tan x}=2 &(2) \\

\textit{e thru} &\tan x=\ln 2 &(3)\\

\textit{isolate x } &x=\arctan \ln 2+\pi n &(4)\\

\textit{[0,1] } &\arctan(\ln 2)=0.606 &(5)\\

\textit{m at x} &y_m=e^{\tan (x)}\sec ^2(x) &(6)\\

\textit{m} &y_m(0.606)=2.96 &(7)

\end{array}$

it took me 2 hours to do this

must be a better way

if its correct:unsure: