Let f be a function defined in the interval (1,\infty) as f(x)=\integral_{e} ^{x^2} t/ln(t) dt. Find the equation of the tangent line to the graph of f at the point whose x-coordinate is sqrt{e}.

The equation of the tangent line to the graph of the function y=f(x) at the point whose x-coordinate is sqrt{e} is given by y-yf=m(x-xf), where xf=sqrt{e}, yf=f(sqrt{e})=integral_{e}^{e} t/ln(t) dt = 0 and m=f'(sqrt{e})=[x^22x/ln(x^2)]x=sqrt{e}=2esqrt{e}/ln(e)=2esqrt{e}. To calculate m we used the Fundamental theorem of calculus.Then, the tangent line has equation y=2esqrt{e}(x-sqrt{e}), so y=2e*sqrt{e}x-2e^2.

RM
Answered by Roberta M. Italian tutor

1400 Views

See similar Italian A Level tutors

Related Italian A Level answers

All answers ▸

Translate the following excerpt from an art textbook (2)


Can you explain me, with examples, what the CONGIUNTIVO tense is and how do you form it?


Translate the following sentence into Italian: I should have known that it was not the right choice. This work does not inspire me, therefore I am going to change career path. I hope that my parents will be proud of me, instead of judging me.


What is the difference between the passato prossimo, the passato remoto and the imperfetto? - See more at: https://www.mytutorweb.co.uk/tutors/secure/ta-yourexplanations.html#sthash.IFYOERg2.dpuf


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences