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I am Lyosha [343]
3 years ago
15

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the give

n point. See Example 5.
y = ln x; (e, e)
Mathematics
1 answer:
Darina [25.2K]3 years ago
3 0

Answer:

x-ey=e+e^2

Step-by-step-explanation:

We are given that  

y=lnx

Point (e,e)

We have to find the equation of tangent line to the given graph.

Differentiate w.r.t x

\frac{dy}{dx}=\frac{1}{x}

By using formula

\frac{d(lnx)}{dx}=\frac{1}{x}

Substitute x=e  

m=\frac{dy}{dx}=\frac{1}{e}

m=\frac{dy}{dx}=\frac{1}{e}

Slope-point form:

y-y_1=m(x-x_1)

x_1=e,y_1=e

By using this formula  

The equation of tangent to the given graph  

y-e=\frac{1}{e}(x-e)

ey-e^2=x-e

x-ey=e+e^2

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<u>Step-by-step explanation:</u>

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