I have solved all questions in my homework except for this question. please give me the solution to this question in 60minutes max.

Let f: R - (0, + oo) be differentiable. Suppose that f has no zero. If lim f(x) = 0, then x-0 lim (csef(x))(x) x-0 Select one: O a. does not exist O b. is 1 O c. None of these three O d. is 0Let f: R - R be a strictly increasing and differentiable function with f(0) = 6, and let g(x) = 2f(x) + arctanx. Which of the following MUST be TRUE? Select one: O a. g has an inverse function h. If f(0)=9.7, then h'(12.0000)=0.0515, where the input of h' is exact while the output is correct to 4 decimal places. O b. None of these three O c. g has an inverse function h. If f(0)=2.5, then h'(12.0000)=0.1667, where the input of h' is exact while the output is correct to 4 decimal places. O d. g has no inverse function\f