Concept explainers
Graphical, Numerical, and Analytic Analysis In Exercises 33–36, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods.
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Calculus
- In Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and asymptotes.arrow_forwardThe process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits in Exercises 23–36.arrow_forwardIn Exercises 11–50, evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits that don't exist indicate whether they can be expressed as = -o or = ∞.arrow_forward
- In Exercises 1–4, show that the limit leads to an indeterminate form. Then carry out the two-step procedure: Transform the function alge- braically and evaluate using continuity.arrow_forwardIn Exercises 49–54, show that the limits do not exist.arrow_forwardIn Exercises 79–82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.) 79. lim f(x) = 0, lim f(x) = ∞, and lim f(x) = ∞ x→too x-2+ 80. lim g(x) = 0, lim g(x) = –∞, and lim g(x) = ∞ x→3- x→3* 81. lim h(x) = -1, lim h(x) = 1, lim h(x) = -1, and x -00 lim h(x) = 1 x→0+ 1, lim k(x) x→l¯ = 00, and lim k(x) x→I* 82. lim k(x) = -00arrow_forward
- Find the limits in Exercises 25–30.arrow_forwardPrecise Definition of Limit In Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.arrow_forwardIn Exercises 4–18,(evaluate the limit)or explain why it does not exist. 4. lim (x² – 4x + 1) 5. lim x 3 x + 6 x + 3 X4arrow_forward
- Assessment 1. Directions: Find the limit of the following. 1. lim(x² + 2x – 1) X-2 2. lim (x³ + 8) x--2arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If it does not exist, enter NONE. a) lim x→3− f(x) b) im x→3+ f(x) c) lim x→3 f(x) d) lim x→7 f(x) e) f(7)arrow_forwardQuestion 2 Evaluate: lim, -1 21²+x-1 x+1 4 ptsarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage