How do you find the equation of the

Breanna Mcclure

Breanna Mcclure

Answered question

2022-04-14

How do you find the equation of the tangent and normal line to the curve y=lnx at x=e?

Answer & Explanation

Mey9ci0

Mey9ci0

Beginner2022-04-15Added 14 answers

Explanation:
y=lnx
y=1 at x=e
y=1x the slope of f(x)=1x
The equation of a straight line with slope (m) passing throught point (x1,y1) is:
(yy1)=m(xx1)
Since m at x=e is 1e
The equation of tangent to f(x) at (e, 1) is
(y1)=1e(xe)
y=xe1+1
y=xe
And equation of normal to f(x) at (e, 1) is
(y-1)=-e(x-e) (Since slope of normal =1m)
y=ex+e2+1
y=e(e-x)+1

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