Recall the procedure for finding lim f(x)9() for indeterminate forms of type 0, co and 10. Note x -+ a that in lim f(x)9(2), the x - a could be replaced with x -+ at, or x - 100. (i) Analyze L = lim g(x) In f(x). Put in form ; or % and use L'Hopital's Rule. (ii) If L is finite, lim f(x)9(x) = el. If L = co, lim f(x)9(x) = co. If L = -oo, lim f(x)(z) = 0. 1. lim x is an indeterminate form of type 0, oo, 10 (circle one). Show that lim x7 = 1. 2. lim xitiz with a > 0, a * 1, is an indeterminate form of type 0, co, 10 (circle one). Show that lim altinz = a. In a 3. lim xitinz with a > 0, a * 1, is an indeterminate form of type 0, co, 10 (circle one). 20 -+00 In a Show that lim x1tiz = a. 2-+00 4. lim (x + 1) : with a > 0, a * 1, is an indeterminate form of type 0, co, 10 (circle one). x -+ 0+ Show that lim (x + 1) . = a. e z 5. lim 1 + - is an indeterminate form of type 0, co, 10 (circle one). x -+00 e I Show that lim = 00. x+ sin(2x) 6. Explain why L'Hopital's Rule is of no help in finding lim Find the limit using methods learned earlier in the semester. 7. Why was it necessary to specify that a # 1 for problems 2, 3 and 4 above