Concept explainers
Finding Limits at Infinity In Exercises 11 and 12, find
(a)
(b)
(c)
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Calculus of a Single Variable
- Use the graph of the function f to decide whether the value of the given quantity exists. (d) lim x→0 f(x) (e) f(2) (f) lim x→2 f(x)arrow_forwardConsider the function:f(x) = {x2, x ≤ 2 {4, 2 < x ≤ 4 {x + 2, if x > 4 (a) Sketch the graph of f(x). Find the following limits:(b) lim x→2+ f(x)(c) lim x→2− f(x) (d) lim x→2 f(x)(e) lim x→4+ f(x)(f) lim x→4− f(x)(g) lim x→4 f(x)(h) lim x→−3 f(x)(i) lim x→5 f(x)arrow_forwardFind lim f(x). lim f(x) = x-2 X-2 (4,3) • (2,4) 2- (6.2) 14 -2-arrow_forward
- Sketch the graph of an example of a function f that satisfies all of the given conditions. lim f(x) = ∞, lim f(x) =5, lim f(x) = -5 6. x→2 x→-2+ x→-2- lim f(x) = 0, lim f(x) = 0, f(0) = 0arrow_forwardGive an example of a function f such that lim f(x) exists but f(0) does not exist. Give also, an example of a function g such that g(0) exists but lim g(x) does not exist.arrow_forwardf(2 + h) – f(2) 2 if f(x) = x² +7. Find lim h h→0 f(2 + h) – f(2) lim (Simplify your answer.) h→0arrow_forward
- Graph f (x) to evaluate lim f(x). x→3 Enter the exact answer. lim f(x) = Number x→3¯ f(x) = 4x - 4 17 x3 x 3arrow_forwardSketch the graph of an example of a function f that satisfies all of the given conditions. lim x→0 (f(x)) = ∞, lim x→3− (f(x)) = −∞, lim x→3+ (f(x)) = ∞, lim x→−∞ (f(x)) = 3, lim x→∞ (f(x)) = −2arrow_forwardSketch the graph of the function (a) Evaluate f(G), ƒ(3), and f(1). (b) Evaluate the limits lim f(x), lim f(x), lim f(x), and x 1+ lim f(x). * 0+ (c) Discuss the continuity of the function.arrow_forward
- Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) = (b) lim g(x) X- 2 (c) lim g(f(x)) = x-3arrow_forwardSketch and label a graph of a function f(x) that has the stated properties:f(-2) = 1 and limx→-2 f(x) = 1f(0) = 3 and limx→0 f(x) = 2f(1) = 4 and limx→1 f(x) does not existarrow_forwarda (a) lim f(x) X-2 (b) lim f(x) X→2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage