6. The following limit questions are quite tricky. Be careful! For example, note that the limit laws only apply if all limits exist. Fully justify your work. You may find the correct answer, but for the wrong reasoning. Graph of f 1 X4 -3 -2 -1 2 (a) lim (f(x) + g(x)) x-1 f(x) x1 g(x) (b) lim O (c) lim g(f(x)) -7-x (d) lim g(f(x)) x 2+ (e) lim f(g(x)) x-1- f(x) x 2 g(x) (f) lim n 6. Find the derivative of (x) = [[(x a)*. k=1 https://www.desmos.com/calculator/shdzbhfwd1 k xn 7. Find the derivative of f(x) = n! n=0 https://www.desmos.com/calculator/whu3jniuix 3 = 9. Find derivative of f(p) -3 -2 Graph of g 2 11 -1 1 2 8. Find the derivative of f(x) xn n!' n=0 assuming that you can differentiate an infinite sum term-wise. Compare the terms of '(x) to those of f(x). Based on your observation, can you guess what function f(x) is? Use the link in the last exercise and set k to a very large number. What do you think is happening? What do the functions you see look like? 3 n = = ln Ip (1 p)-xi -P)-.). Simplify using the laws of logarithms before differ- entiating. Note that the values x, should be treated as unknown constants, while p is the variable of differentiation. i=1