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We evaluate the limit of e^x/x^2 as x goes to infinity using L'Hospital's rule. We'll try evaluating the limit and find it has an indeterminate form infinity/infinity. Thus, we take the derivatives of the numerator and denominator and apply L'Hospital's rule. Again we'll find an indeterminate form, so we'll have to use L'Hospital's rule repeatedly. A second application will finish the problem. Let me know if you have questions on how to use L'Hospital's rule! #Calculus1 Limit of (e^x-1-x)/x^2 with L'Hospital's Rule Twice! • Limit of (e^x-1-x)/x^2 with L'Hospital's R... Calculus 1 playlist: • Calculus 1 Calculus 1 Exercises: • Calculus 1 Exercises ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: / wrathofmathedu ● Facebook: / wrathofmath ● Twitter: / wrathofmathedu My Music Channel: / @emery3050