Answer to Question #334711 in Calculus for Leena

Question #334711

Provide all detailed steps to find the limit of the following functions.

Lim x→∞ (e4x - e-2x) ÷ (ln(x+1)


1
Expert's answer
2022-05-03T16:46:00-0400
limxe4xe2xln(x+1)\lim\limits_{x\to \infin}\dfrac{e^{4x}-e^{-2x}}{\ln(x+1)}

Use L'Hôpital's rule


limxe4xe2xln(x+1)=limx(e4xe2x)(ln(x+1))\lim\limits_{x\to \infin}\dfrac{e^{4x}-e^{-2x}}{\ln(x+1)}=\lim\limits_{x\to \infin}\dfrac{(e^{4x}-e^{-2x})'}{(\ln(x+1))'}

=limx4e4x+2e2x1/(x+1)=limx(4e4x+2e2x)(x+1)=\lim\limits_{x\to \infin}\dfrac{4e^{4x}+2e^{-2x}}{1/(x+1)}=\lim\limits_{x\to \infin}(4e^{4x}+2e^{-2x})(x+1)

==\infin


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