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Evaluating limits graphically Sketch a graph of f and use it to make a conjecture about the values of
23.
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
- A step function Let f(x) = |x| /x , for x ≠ 0.arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) -4. 2 4 lim f(x) x-2 (a) lim f(x) (b) x- 2* (c) lim f(x) x- 2 (d) f(2) (e) lim f(x) x-4 (f) (4)arrow_forwardMath advancearrow_forward
- -t+2 Evaluate the lim (-2)arrow_forwardThe graph below is the function f(x) 4- 2- -3 -2 -1 -21 -51 Determine the following values. Enter "DNE" if a value does not exist, enter "oo" (lower case "o") if the limit approaches positive infinity, or "-oo" if the limit approaches negative infinity. lim f(x) = lim f(x) = lim f(2) = f(3)arrow_forwardHow do I do A, B, and C?arrow_forward
- Limits of even functions A function f is even if f1-x2 = f1x2, for all x in the domain of f. Suppose f is even, with lim f1x2 = 5 and lim f1x2 = 8. Evaluate the following limits. %3D xS2+ xS2 a. lim f1x2 xS-2+ b. lim f1x2 xS-2-arrow_forward8 5 4 3 2 -2 -1 0 1. 12 6 8 9 10 11 12 13 14 1. Does the lim f(x) exist? Justify. 2. Does the lim f(x) exist? Justify. x -00arrow_forwardB. LIMITS at INFINITY Recall your lesson in Piece-wise function. X→C In this lesson, you must be able to differentiate between f(c) and lim f(x). In evaluating a function f(c), when you do DIRECT SUBSTITUTION, the result must be a DEFINED NUMBER (A NUMBER THAT EXIST), otherwise f(c) is UNDFINED. Contrary to lim f(x), when you do direct substitution, the answer maybe indeterminate 0/0 but THERE IS A WAY TO EVALUATE THE LIMIT USING MANY TECHNIQUES, otherwise lim f(x) DOES NOT EXIST. x→c X-C Let us examine the piece-wise function below. 0 1. f(-4) 2. f(-2) 3. f (0) The function is defined by the equation. 4. f (1) 5. f(2) 6. f (3) f(x) = 2+7, -4≤x≤-2 -2, 7. f (4) 8. f(7). -1, (x-2)², x-4 x-7 7 A Self-Regulated Learning Module 2arrow_forward(3+h)²-9 Evaluate lim h-0 harrow_forwardand radical) What I Know Multiple Choice. Directions: Encircle the letter of the correct answer. 1. Which mathematical expression corresponds to the statement "the limits of the function x2 + 2 as x approaches to 3 is equal to 11"? C. lim (x2 + 2) = 11 x →3 А. lim (x2 + 2) = 11 D. lim (x² – 2) = 11 x -3 X--3 В. lim (x2-2) = -11 x--3 2. Which function becomes undefined? f(x) = 0 C. f(x) = L D. f(x) = ; b= 0 А. В. X = c 3. What is the value of m(x² - 3x +4)? А. С. 2 В. D. 1 4. Which of the following denotes the definition of limit of a function? А. lim f(x) = L C. x approaches c as L В. f(x) approaches L D. lim f (x) = x 5. Graphing the limit of the f(x) = 1 %3D as x approaches to zero, which statement is correct? A. The limit of the function is equal to zero. B. The limit of the function does not exist.arrow_forwardarrow_back_iosarrow_forward_ios
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