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Determining Continuity In Exercises 11– 40, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. See Examples 1, 2, 3, 4, and 5.
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Calculus: An Applied Approach (Providence College: MTH 109)
- example to prove 2. Show that a constant function is continuous. Present an the proof.arrow_forwardExercises 101–103 will help you prepare for the material covered in the next section. Use the graph of function f to solve each exercise. 5- 4- 3- 2- 1- -5-4 1 2 3 45 y = flx) 101. For what values of x is the function undefined? 102. Write the equation of the vertical asymptote, or the vertical line that the graph of f approaches but does not touch. 103. Write the equation of the horizontal asymptote, or the horizontal line that the graph of f approaches but does not touch.arrow_forwardStudy the continuity of the following functions and show the process of how you tell if it is continued or discontinuedarrow_forward
- Write the function in partsarrow_forwardDifferentiate the function. f(x) = x In x -xarrow_forwardExercises 125-130: Evaluate the expression for the given function f. 125. f(a + 2) for f(x) = 3 – 4x² 126. f(a – 3) for S(x) = x² + 2x 127. f(a + h) for f(x) = x² – x + 5 128. f(a – h) for {(x) = 1 – 4x – x² 129. f(a + h) – f(a) for f(x) = 2x² + 3 130. f(a + h) – f(a) for f(x) = x – x²arrow_forward
- Explain using theorems 4, 5, 7 and/or 9 from section 2.5, why the function f(x) = sin x + Inx is continuous at every number in its domain. Make sure to state the domain of the function and state the domain of each function you state is continuous.arrow_forwardPart A: What is the domain and range of f? Enter −∞ as -INF, ∞ as INF, and ∪ (union) as U. Part B: Find f(-2) Part C: Find f(2)arrow_forwardHow to know if y is a function of x.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell