I really need help with this step by step answers so I can under it and see where I did wrong please.

05:01 -fleet02-xythos.content.blackboardcdn.com C 1 of 2 lath 140 Review sheet for Test 1 The exam will contain a number of problems, of types similar to the problems given in this review sheet (but not that many). Please prepare for each problem type. 1. Compute the limit or show that it does not exist. If the limit does not exist, indicate whether it co, -0o, or neither. 2x- - 3x + 1 (a) lim 3-212 + x answer: -90 (c) lim 3+1 - 3 * +2 x-2 answer: - x2 - 25 (b) lim *+ 5 x3 + 125 answer. - 15 (d) lim V5+h- v5 answer: 275 2. Evaluate the following limits. (a) lim . +x x-+00 2x2 + 5 answer: (c) lim answer: 0 3x3 + x2 (b) lim 2,245 answer: - (d) lim 1+ 6er answer: 4 3. Use the following graph of y = f(x) to evaluate the following lim f(x) = lim f(x) = lim f (x) = f (2) = 4. Use the following graph of y = f(x) to evaluate the following. lim f(x) = lim f(x) = lim f (x) = f(1) = Math 140 Review sheet for Test 1 5. Is it possible that f(4) = 7 and lim,-+4 f(x) = 8? Either explain why it is not possible, or discuss the circum- stances that make it possible. 6. Suppose that lim,-,1+ f(x) = 5. What else needs to be true in order for f to be continuous at 1? 7. What does a have to be in order for the following function to be continuous? f ( x ) = 3x+1 ifx52 "(x ta ifx > 2' 8. Consider the following argument: "If f(x) = -, then f(-2) = -1/2 and f(2) = 1/2. Since f(-2) is negative and f(2) is positive, the Interme- diate Value Theorem says that f(x) has a root between x = -2 and x = 2." Is this argument valid? Why or why not? answer: The function is not continuous 9. Use Intermediate Value Theorem (IVT) to show that there is a solution to the given equation in a specified interval (a) x - 3x = 10, where x E (1,2) (b) xcosx = sin 2x + 3, where x E (0, 27) 10. Recall the definition of the derivative of f at a: f'(a) = lim ! (a +h) -f(a) (a) Let f(x) = (3x - 1)2. Use the above definition to calculate f'(0). answer: S'(0) = -6 (b) Let g (x) = x+ 1. Use the above definition to calculate g'(1). answer: g' (1) = 1/4 11. Differentiate (find the derivative) (a) x(x -2x) answer: 4x' - 4r (c) 21+ 1 answer: 724+1) 3x2 + 52 (b) x2(5-x3) answer: 10x - 5.14 (d) y = 3. answer: 12. Find an equation of the tangent line to the given curve at the specified point. (a) y= 23 - 5x2 + 3x +4 atx = 2 answer:y=7x-8(b) y = 21 atx= =1 answer: y = - 1 13. Consider the table below. * f ( x ) f ( x ) 8 ( x ) 8' ( x ) 2 5 3 2 (a) Find h'(1) if h(x) = f(x)g(x). answer: 5 (b) Find q (2) if q(x) = 8(x)/f(x). answer: 41/25 K m