6.5 c) limit (cos x) / x where x to pi d) limit x*sin(1/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 i) limit (cos x)/(cos x -1) where x to 0 6.20 b) plot sqrt(x/(x-2)) d) Plot[Piecewise[{{x^3, x<2}, {4 x, x>2}}],{x,-1,4}] 6.21 c) Plot[Piecewise[{{3+(-1)*x^2, x<=1}, {x+1, x>1}}],{x,-1,2}] d) Plot[Piecewise[{{x-2, x<=1}, {cos(pi*x), x>1}}],{x,0,2}]