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T3-EOY-MAT70 10- Choose the correct answer Hint on steps to follow: Find f(x) or df/dx Then f(x) Then f(x) (the given integ
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Answer #1

Following the give steps lets first find out the function f as

The given integral is

f(x)=\int_{0}^{x} e^t dt = \[e^t\]_{0}^{x}=(e^x-e^0)=e^x-1

so,

f(3) = e - 1

f(2)=e^2-1

f'(x)=e^x+0=e^x

f'(2)=e^2

Plug these values in the equation of tangent  y-f(x_0)=f'(x_0)(x-x_0)

[here \; x_0 = 2]

we have

y-f(2)=f'(2)(x-2)

\implies y-(e^2-1)=e^2(x-2)

\implies y-e^2+1=xe^2-2e^2

\implies y=xe^2-2e^2+e^2-1=xe^2-e^2-1

Hence, y=xe^2-e^2-1

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