Determine the following limit using L'Hopital's Rule, where appropriate. Be sure to include a justification for why you can use L'Hopital's Rule each time you use it. 1. 2. € ¹n ( 1 + ¹ ) X lim √x ln(1 + X→∞ tan-¹ x lim xt x→0+

Q: x' +4 a. lim X-4 x-2 %3D x² -1 b. lim- xl x' -1 Vx - Ja lim- с. х —а

Q: Evaluate the following limit: lim 04-x (sin x - x + x + ¼ x³) (eª − 1) x6 : Do not use L'Hospital's…

Q: f(x) = cot Create a table of values for the function. (Round your answers to two decimal places.)…

Q: 1. Evaluate: lim (lnr) h-0+

Q: . Evaluate the limit by using a change of variable. 27 X 1 3 b. lim x-27 c. lim X² 1 X6 1 - X→1 X 1…

Q: 8. Evaluate the limit by using a √√x-2 a. lim x8x8

Q: lim ln(7-x) x →7

Q: 12. Evaluate the following limits. Use L'Hospital's Rule if it applies. a. lim- b. lim c. lim(x)

Q: Complete the table and use the result to estimate the limit. Use a graphing utility to graph the…

Q: Using the limit definition of the derivative (lim Eth)=/=) to sove for the following: a. f(x) = x²…

Q: For each part of this question, refer to the graph of g(x) shown below. 6 -6 -5 -4 a. lim g(x) Z-1…