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10.) For the natural logarithm function, determine the point on the curve where its associated tangent line passes through the
origin as depicted in this diagram.

10 For the natural logarithm function determine the point on the curve where its associated tangent line passes through the origin as depicted in this diagram class=

Respuesta :

f(x)=lnx

y=f(x)

dy/dx= 1/x

tangent at (x,y) has slope 1/x

eqn of tangent is y = mx + c

since the tangent passes through origin, c=0

substitute y = lnx and m= 1/x to above eqn

lnx = 1

x=e

y=lne=1




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