Page:Calculus Made Easy.pdf/279

(11) Max. and min. for $x=7.5$, $y=\pm 5.414$. (See example no. 10, here.)

(12) Min.: $x={\tfrac {1}{2}}$, $y=0.25$; max.: $x=-{\tfrac {1}{3}}$, $y=1.408$.

 

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Exercises XI. (p. 130.)

(1) ${\dfrac {2}{x-3}}+{\dfrac {1}{x+4}}$.

(2) ${\dfrac {1}{x-1}}+{\dfrac {2}{x-2}}$.

(3) ${\dfrac {2}{x-3}}+{\dfrac {1}{x+4}}$.

(4) ${\dfrac {5}{x-4}}-{\dfrac {4}{x-3}}$.

(5) ${\dfrac {19}{13(2x+3)}}-{\dfrac {22}{13(3x-2)}}$.

(6) ${\dfrac {2}{x-2}}+{\dfrac {4}{x-3}}-{\dfrac {5}{x-4}}$.

(7) ${\dfrac {1}{6(x-1)}}+{\dfrac {11}{15(x+2)}}+{\dfrac {1}{10(x-3)}}$.

(8) ${\dfrac {7}{9(3x+1)}}+{\dfrac {71}{63(3x-2)}}-{\dfrac {5}{7(2x+1)}}$.

(9) ${\dfrac {1}{3(x-1)}}+{\dfrac {2x+1}{3(x^{2}+x+1)}}$.

(10) $x+{\dfrac {2}{3(x+1)}}+{\dfrac {1-2x}{3(x^{2}-x+1)}}$.

(11) ${\dfrac {3}{(x+1)}}+{\dfrac {2x+1}{x^{2}+x+1}}$.

(12) ${\dfrac {1}{x-1}}-{\dfrac {1}{x-2}}+{\dfrac {2}{(x-2)^{2}}}$.

(13) ${\dfrac {1}{4(x-1)}}-{\dfrac {1}{4(x+1)}}+{\dfrac {1}{2(x+1)^{2}}}$.

(14) ${\dfrac {4}{9(x-1)}}-{\dfrac {4}{9(x+2)}}-{\dfrac {1}{3(x+2)^{2}}}$.

(15) ${\dfrac {1}{x+2}}-{\dfrac {x-1}{x^{2}+x+1}}-{\dfrac {1}{(x^{2}+x+1)^{2}}}$.

(16) ${\dfrac {5}{x+4}}-{\dfrac {32}{(x+4)^{2}}}+{\dfrac {36}{(x+4)^{3}}}$.

(17) ${\dfrac {7}{9(3x-2)^{2}}}+{\dfrac {55}{9(3x-2)^{3}}}+{\dfrac {73}{9(3x-2)^{4}}}$.

(18) ${\dfrac {1}{6(x-2)}}+{\dfrac {1}{3(x-2)^{2}}}-{\dfrac {x}{6(x^{2}+2x+4)}}$.

 

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