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.: $$x=-\tfrac{1}{3}$$, $$y=1.408$$.

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