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- Which of the following statements about the function y = ƒ(x)graphed here are true, and which are false? limx →cƒ(x) exists at every c in the open interval (-1, 1).Given that the graph of y = f(x) lies between the graphs of y = I(x) and y = u(x) for all x, use the Squeeze Theorem to find lim u(x) = |xl, I(x) = -|x|, f(x) = (1 - cosx)/x x->0Find the limit of f(x) , [3f(x)], and [f(x)]2, as x approaches c.
- Which of the following statements about the function y = ƒ(x)graphed here are true, and which are false? limx →0ƒ(x) exists.Which of the following statements about the function y = ƒ(x)graphed here are true, and which are false? limx →cƒ(x) exists at every point c in (-1, 1).Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can limt-->0 (g(t))/(h(t)) exist? If it does exist, must it equal zero? Give reasons for your answers
- Let g be defined on an interval A, and let c ∈ A. (a) Explain why g'(c) in Definition 5.2.1(Differentiability) could have been given by g'(c) = limh→0g(c + h) − g(c)/hShow that an is decreasing and bounded from below where an+1 = (1+a^2n)/3 and a1 = 1. Then determine lim n→∞ an.Find the linearization L(x) of f(x) at x=a.