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Mathematics

OpenStudy (anonymous):

find an equation of the tangent line to the graph of y=xlnx at the point (1,0)

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myininaya (myininaya):

\[y'=(1) \ln(x)+x \frac{1}{x}=\ln(x)+1\]

myininaya (myininaya):

\[y'|_{x=1}=\ln(1)+1=0+1=1\]

myininaya (myininaya):

\[y=x+b\]

myininaya (myininaya):

we need to find b the y-intercept

myininaya (myininaya):

we know a point on this line: (1,0)

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myininaya (myininaya):

0=1+b=> -1=b=> b=-1

myininaya (myininaya):

\[y=x-1\]

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