Concept explainers
Finding a Limit In Exercises 37–42, find a formula for the sum of n terms. Use the formula to find the limit as n
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Calculus
- 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_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 75–78, sketch the graph of a function y = f(x) that satis- fies the given conditions. No formulas are required-just label the coordinate axes and sketch an appropriate graph. (The answers are not unique, so your graphs may not be exactly like those in the answer section.) 75. f(0) = 0, f(1) = 2, f(-1) = -2, lim f(x) = -1, and x--00 lim f(x) = 1 76. f(0) = 0, lim f(x) = 0, lim f(x) = 2, and lim f(x) = -2 x→0* %3D 77. f(0) = 0, lim f(x) = 0, lim f(x) = lim f(x) = ∞, x-too x→1- x--1+ = -0, and lim f(x) = -∞ lim f(x) x→1* 78. f(2) = 1, f(-1) = 0, lim f(x) = 0, lim f(x) = ∞, x→0* lim f(x) = -00, and lim f(x) = 1 X -00arrow_forward
- functional analysis 4 find the limit of the following sequences in given spacearrow_forwarde -1-z lim 20arrow_forwardIn Exercises 29– 44, determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit:- see the equation as atached herearrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage