Concept explainers
Evaluating limits graphically Sketch a graph of f and use it to make a conjecture about the values of
24.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
- A step function Let f(x) = |x| /x , for x ≠ 0.arrow_forwardLimits 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_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_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_forwardFind the value of -3 in the tablearrow_forward(3+h)²-9 Evaluate lim h-0 harrow_forwardusing this graph find the limit as x approaches -4- of f(x)arrow_forwardLet |22² − a²| x-a 3 12 Find the lim f(x) x-a- Find the lim x→a+ if x < a (x + a)² if x ≥ a explanation how you get your answer in each case. 3 f(x) = f(a) x-a 4 For what value(s) of a, lim f(x) = lim f(x) = f(a). x-a x→a 5 where a is some constant. Show all your work or give a brief LO 6arrow_forwardx+ y3 Consider lim Which ONE of the following statements is TRUE? (x.y)-(1,-1) x+y A. None of the choices in the list. B. For every number e>0 there is a corresponding number 8>0 such that if point (x,y) is in the domain of f (x,y) = - and 00 there is a corresponding number 8>0 such that if point (x.y) is in the domain of f(x.y) = and 00 there is a correspomding number &>0 such that if point (x,y) is in the domain of f (x,y) = - x+y and 0<(x-1)2+ (y+1)? <8 and then |f (x,y) – 3|arrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning