I need help from question 1 to question 7 and want you to also show your work, please.

1. (12 points) Evaluate the limit algebraically if it exists. (Do not use Table method for parts a, b) x-36 lim a. X-+36 Vx - 6 x-7 lim b. X-+7 x- -492. (10points) Explain why the function is continuous at every number in its domain. Then, state the domain. 2x- - x-1 F (x) = x- -43. (16points) Find the limit or show that it does not exist. [Hint: use Theorem 5 for both parts a, b] x - 2x lim a. 3x4 -3x- + x b. lim x*- x+2x' -4) 4. (14points) Find the value of the lim (x -2) by constructing tables of values. (Write the results correct to four decimal places. Write your conclusion at the end. Use your graphing calculator for quicker results. Left side of x - 4 right side of x =2 V= (x2 -4 (x-2) x = 2 (x -2) 1.5 2.5 1.9 2.1 1.99 2.01 1.999 2.001 1.99999 2.00001 Conclusion: x- -4 lim x-+2 (x - 2)5. The graph of a function is given below. Discuss what type of discontinuity this function has and at what x-values. Explain the reason why it is discontinuous. (16points) VA 5 - y = f(x) 0 5 76. Find the limit algebraically. [Hint: use either direct substitution and/or simplifying/multiply by the conjugate]. (10 points) x -9 lim max +2x-37. For the function / (x) whose graph is given below, state the following: (22 points) a. lim / (x) = b. lim /(x)= c. lim /(x) = d. lim / (x) = e. lim / (x] = f. lim (@)= g. lim / (x] = h. lim /(x)= i. lim /(x)= j. lim / (x) = K. NO)= 0 1Instructions: Read this first . You may use your calculator TI 83 or 84 plus to aid you in solving problems and checking your work. However, to earn full credit, you must show work and/or provide an explanation of how you arrived at your final answer (A correct answer without justification or appropriate work is worth zero points). . Use Calculus I methods ONLY discussed in class. Any method borrowed from the internet that is not discussed in class will not be considered and/or accepted. . Your work must be organized, and questions' answers must be listed in order before scanning and uploading them to canvas. Neatness and completeness count. Write answers in exact form Do NOT write more than two questions on the same page, and do NOT write on the back of a page if you are using your own papers . Do not use graph paper to write your solution on it as it is hard to grade on canvas. Instead, either use plain white paper or lined papers (I prefer if you print this document and write on it) . The HONOR CODE. By signing my name in the blank above, I acknowledge that I understand that for this test no assistance is allowed (from phone apps, internet, chat, etc..). It would be cheating and a violation of the student code of conduct which could result in a failing grade or worse. But in this crazy remote teaching environment it is just not cool and will be a great hinderance to my success in Calc 2, physics and other advanced classes. ANOTHER WAY TO UPLOAD PDF FILES on canvas 1. Download any free PDF scanner app on your phone such as "CamScanner". 2. Take photos (make the camera on top of the paper instead of tilting it at a degree) of your assignments using the app in order, Questions 1, 2, 3, etc... 3. Save the PDF to your phone 4. Email the PDF to yourself (sometimes you can do this directly through the app in step 3) 5. Download the PDF onto your computer. 6. Upload the PDF to canvas