6.5 c) limit (cos x) / x where x to pi d) limit x*sin(1/x) where x to 0 j) limit |x|/x where x to 0 6.6 c) limit (x^2+x)/(x^3+1) where x to -1 d) limit (x^2-2x-3)/(3-x) where x to 3 j) limit (x+1)/(sqrt(x^2-4)) where x to -1 6.7 a) limit (sqrt(x)-1)/(x-1) where x to 1 g) limit (x-sqrt(x^2-x)) where x to infty plot (x-sqrt(x^2-x)) where x from 0 to 100 6.8 b) limit x^2/(x+1) where x to infty plot x^2/(x+1) where x from 0 to 100 d) limit sqrt(x^2+1)/(x) where x to -infty plot sqrt(x^2+1)/(x) where x from -1 to -100 h) limit 1/(x^2-7x+1) where x to infty plot 1/(x^2-7x+1) where x from 0 to 100 6.15 e) limit (1-cos x)/x^2 where x to 0 i) limit (sin(3x))/x where x to infty plot (sin(3x))/x where x from 1 to 100 n) limit ((x+1)/(x-2))^(3x-2) where x to -infty plot ((x+1)/(x-2))^(3x-2) plot e^9 where x from -10000 to 0 6.16 b) limit (x+2)/(1-sqrt(x+3)) where x to -2 d) limit (sqrt(x^2-4x)+x) where x to -infty e) limit (x^2*sin(1/x))/(sin x) where x to 0 i) limit (cos x)/(cos x -1) where x to 0 6.18 Plot[Piecewise[{{3x, x<1}, {3, 3>=x>1}, {0, x>3}}],{x,0,5}] 6.20 b) Plot[Piecewise[{{4/3*x^2, x<2}, {2*x+4/3, x>2}}],{x,0,4}] d) Plot[Piecewise[{{x-2, x<1}, {cos(pi*x), x>1}}],{x,-1,3}] 6.21 b) plot (sin x)^2/x c) plot 2^(1/(3-x)) where x=2..4 y=-100..100 d) plot (1+x)^(1/x) h) atan (1/x)