lim-0-2-e-2t-t-dt-

Question Number 217626 by mnjuly1970 last updated on 17/Mar/25

\lim_{λ \to 0} \int_{λ}^{2 λ} \frac{e^{2 t}}{t} d t = ?

Answered by maths2 last updated on 17/Mar/25

= \lim_{x \to 0} \int_{x}^{2 x} \frac{e^{2 t} - 1}{t} + \frac{1}{t} d t

= \lim_{x \to 0} {\int_{x}^{2 x} \frac{e^{2 t} - 1}{t} d t + \int_{x}^{2 x} \frac{1}{t}} d t

= l n (2) + \lim_{x \to 0} \int_{x}^{2 x} \frac{e^{2 t} - 1}{t} {d t}_{= 0}

t \overset{\overset{*}{f}}{\to} \frac{e^{2 t} - 1}{t} c a n b e e d e f i n d a s c o n t i n s f u n c t i o n o v e r

You can't use 'macro parameter character #' in math mode

\lim_{x \to 0} \int_{x}^{2 x} \frac{e^{2 g}}{g} d g = l n (2)

Commented by mnjuly1970 last updated on 17/Mar/25

t h a n k s a l o t s i r .

Commented by maths2 last updated on 17/Mar/25

W i t h e P l e a s u r G o d B l e s s Y o u

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