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Example 3
Find the co-ordinates of the point of contact of
the tangent line to the curve y = x log x, which is inclined at
an angle of 450 with the x-axis
Solution : Let P(x,y) be the point
of contact
The curve is y = x log x
\ Slope
of the tangent at P = 1 + log x ®(1)
Since this tangent has inclination of 450 with x-axis, its slope is
\
tan 450 = 1 ® (2)
\
1 + log x = 1 ® [from 1 and
2]
\
log x = 0 Þ x = 1
But P lies on the curve
y = x log x \ y = 1 log 1 =
0
\ P has co-ordinates
= ( 1,0 )
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