8.1     a) lim(sqrt(x)-5), x to 25
        b) lim(1/x), x to 0
        c) lim(|x|/x), x to 0-
        d) lim(x*sin(1/x)), x to 0
        e) lim(2x^2+sqrt(x)-sin x^3), x to inf
        f) lim(arctan(1-x)), x to inf
        g) lim(ln(sin(x))), x to 0+
        h) lim(0.1^(pi/x)), x to 0+
        i) lim(e^(1/x)), x to 0-
        j) lim(3^x/2^(1/x)), x to 0-

8.2     a) lim(((x-2)^2-1)/(2x-2)), x to 1
        b) lim((x^2-9)/(x^2-3x)^2), x to 3
        c) lim((x^3-8)/((2x^2-8)x^2)), x to 2
        d) lim(((x+2)sqrt(x))/(x-sqrt(x))), x to 0+
        e) lim((sqrt(x-4)-1)/(x-5)), x to 5
        f) lim((x+2)/(1-sqrt(x+3))), x to -2
        g) lim((sqrt(x)-3)/(sqrt(2x+7)-5)), x to 9

8.3     a) lim((3x)/(x-4)), x to inf
        b) lim((x^2)/(x+1)), x to inf
        c) lim((2x^2+4)/(x^4-x+1)), x to inf
        d) lim((2x^3+3)/(5x^2+7)), x to -inf
        e) lim((sqrt(x^2))/(x+1)), x to -inf
        f) lim((sqrt(4x^4+5))/(x*sqrt(x^2+x-3))), x to -inf
        g) lim((x*(3x+2)*(x^2-x+7))/(2x+1)^3), x to inf

8.4     a) lim(log_10(x)-log_10(2x)), x to 0+
        b) lim(1/x-1/x^2), x to 0
        c) lim(sqrt(x^2+x)-x^2), x to inf
        d) lim(sqrt(x^2+3x)-x), x to inf
        e) lim((arctan(x))/(x-sqrt(x^2-x))), x to inf
        f) lim(sqrt(9-x)-sqrt(4-x)), x to -inf
        g) lim((sqrt(x^2-4x)+x)/(x+sqrt(x^2+5x))), x to -inf

8.5     a) Plot[Piecewise[{{x^3, x<2}, {6, 2.1>x>=2}, {4x, x>=2.1}}],{x,0,4}]
        b) Plot[Piecewise[{{pi/2+arctan(1/x), x<0}, {0, 0.1>x>=0}, {2*e^(ln(3x)), x>=0.1}}],{x,-2,2}]

8.6     a) Plot[Piecewise[{{(2x-6)^2/(x^3-9x), x<=3}, {0*x^2, x>3}}],{x,0,6}]
        b) Plot[Piecewise[{{ln(3-1*x), x<=2}, {(x-2)/(x-1*1), x>2}}],{x,0,6}]
        c) Plot[Piecewise[{{ln(2*e^2*x)-ln(1+x), x<=1}, {2^x, x>1}}],{x,0,6}]