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Section 5.2 »

Section 5.1

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1. \displaystyle{\lim_{h \to 0}\frac{\tan^2(h)}{h} = 0}

3. \displaystyle{\lim_{h \to 0}\frac{h^2\sin(h)}{h^2} = 0} and \displaystyle{\lim_{h \to 0}\frac{h^2\sin(h)}{h^3} = 1}

5. \displaystyle{\lim_{h \to 0}\frac{\sin^2(3h)}{h^2} = 9}

7. (a) \displaystyle{P_4(x) = 2x - \frac{4x^3}{3}}

(c) \displaystyle{P_4(z) = 2 + \frac{1}{4}(z - 4) - \frac{1}{64}(z - 4)^2 + \frac{1}{512}(z - 4)^3}
\displaystyle{- \frac{5}{16384}(z - 4)^4}

(e) \displaystyle{P_4(x) = -(x - \pi) + \frac{1}{6}(x - \pi)^3}

(g) \displaystyle{P_4(x) = 1 - (x - 1) + (x - 1)^2 - (x - 1)^3 + (x - 1)^4}

(h) \displaystyle{P_4(x) = -9 + 2x + 3x^2}

(i) \displaystyle{P_4(x) = 1 - x^2 + x^4}

(k) \displaystyle{P_4(t) = 1 - 2(t - 1) + 3(t - 1)^2 - 4(t - 1)^3 + 5 (t - 1)^4}

(m) \displaystyle{P_4(t) = 1 + \frac{1}{4}t^2 + \frac{5}{24}t^4}

(n) \displaystyle{P_4(x) = -5 - (x - 1) + 7(x - 1)^2 + 8(x - 1)^3 +3(x - 1)^4}

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