BASIC CALCULUS WRITTEN WORK #2 FIRST GRADING, SECOND SEMESTER PAGE NAME. GRADE & SECTION General Instructions: This is a written work worth 30 points. Cut this part (broken lines) and staple them property and submit them in school of (this is encouraged) take clear pictures of scan your answer sheets and upload them to GENYO. Don't Forget to write your name grade and section on the upper left corner of the next pages. ALL final answers should be written in blue or black ink only strictly NO any kind of ERASURE or change in answer, NO superimposition on final answers. I TRUE OR FALSE: Write TRUE if the statement is always correct, otherwise, FALSE. Write your answer on the space provided before each number. (7 points) 1. When evaluating the limit of a function using substitution yields an indeterminate form, the limit cannot be determined. 2. The limit of the function g(x) = pas x approaches zero exists and it is +03. 3. lim /(x) = 5 means that x approaches 5 from the left or the right of 1=-6. 4. Given the function, f(x) = my , the limit of the function as x approaches - 2 is negative infinity. 5. If / (a) does not exist and lim / (x) exists, then there is a removable discontinuity at a. 6. If lim f(x) # lim f(x), then f has a jump discontinuity at a if and only If their limit exists. 7. f (x) = /x) is continuous everywhere. II. MULTIPLE CHOICE: Choose the correct alternative that satisfies the given question. Write your answers in CAPITAL LETTERS on the blanks provided for. If there is no answer from the given choices, write NA. Some numbers may require showing your solution. (8 points) 1. The figure shows the graph of a function f (x) with domain 0 S x $ 3. Which of the following statements are true? I) lim / (x) exists 1) lim f(x) exists *+2+ Ill) lim f (x) exists (A) I only (B) II only (C) I and II only (D) II and Ill onlyBASIC CALCULUS PAGE 49 2. Which is the interpretation of the statement lim / (x) = 1 7 I. For all x values close to c, but not equal to c, the values of / (x) approach a single finite value L. Il. For all x values close to c, but not equal to c. the values of / (x) approach two finite values of L. lil. For all x values close to c, but not equal to c, the value of / (x) does not exist. (A) i only (B) I and II only (C) ii and lil only (D) | and lii only 3. What is lim 1 1, (A) 2 (B) 4 (C) 8 (D) does not exist 4. Given / (x) = x - 3x, what is Im (3+h)-/(2) , (A) 2x + 3 (B) 2x - 3 (C) 2x (D) 0 5. Let f(x) be the function / (x) = ( -c if x 1 continuous? (A) (0,1] (B) [0, 1] (C) (1,2) (D) [-1,2]