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kwal0203
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Homework Statement
Show that, for each real number t [itex]\in[/itex] the interval (0, 1], the curve given by:
[itex]y=ln(\frac{x+\sqrt{1+x^{2}}}{1+\sqrt{2}})[/itex]
has a tangent line with slope t. Find the points on the curve at which the tangent line has slope 2/3.
The Attempt at a Solution
I found the first derivative of this curve to be:
[itex]dy/dx=1/\sqrt{(1+x^{2})}[/itex]
but now not sure how to proceed.
What do they mean when they ask me to show that for each t has a tangent line with slope t?
any help appreciated!
Also to find the points with dy/dx=3 I did this:
[itex]dy/dx=1/\sqrt{(1+x^{2})} =2/3[/itex] >>>> [itex]x=\pm \sqrt{5}/2[/itex]
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