oblems. 1. Graph f(x) = 25 - 5x4 + 5x3 using the eight-step method. Try not to use a calculator. 2. Graph f(x) = 4_273 _2 4 27 using the eight-step method. Hint 1: You can use a calculator for this problem, as some calculations would otherwise be extremely difficult. Hint 2: The equation f"(x) = 0 has only one solution in the domain of f, let's call it do. It is extremely difficult to find, and you do not need to do so. Instead, use the fact that do ~ -3.5 and f(do) ~ 0.7. 3. Compute lim 1 + x arccosa - V1 - x2 with full justification. 1. Suppose f: R - R is a differentiable function that has the following properties: a. lim f(x) = 0 b. lim f(x2) = 0 c. lim f'(x) = 1 d. lim f'(x]) = = e. f'(x2) # 0 on (1.5, 2.5). Compute lim f(x) x-2 f(x2) - with full justification. 5. Compute lim (csc(x3) - csc(x3) cos(26) ) with full justification. 6. Compute lim re-2/2 with full justification. I-+00 7. Compute lim | sinx with full justification. 8. Observe that lim tan r - sinc sec2 x - 1 is a "zero/zero type" limit that can be solved using algebraic manipulation (think: trigonometric identities) or L'Hospital's Rule. Compute this limit using both approaches. Which method do you prefer? 9. Observe that lim sin( + 7) is a "zero/zero type" limit that can be solved using algebraic manipulation (think: sinc trigonometric identities) or L'Hospital's Rule. Compute this limit using both approaches. Which method do you prefer