Limits: The Concept and Its Role in Mathematics; an Introductory Treatment |
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a₁ An+1 approaches a limit approaches zero asymptote axis band becomes infinite Calculate called Chapter chosen circle commutative law Consider constant corresponding countable curve decimal denoted derivative difference difference quotient digits discontinuity distance divergent series domain e band equation Evaluate Example Exercises fact fractions function defined geometric series given graph harmonic series Hence illustrated inequalities infinite series irrational number lim f(x limit exists margin mathematics maxima and minima maximum means minimum monotone increasing neighborhood notation nth term number line ordered pairs polynomial positive integers positive number positive-term series problem proof prove that lim radians ratio test rational functions rational numbers rational points real numbers rectangle requires satisfied secant line sequence series converges set of numbers Show sketched in Figure slope Solution square strips subinterval symbol tangent test-ratio theorem value of f(x variable word