#1) find limit as x approaches -3 for the function y=x+4
show(limit(x+4,x=-3))
show(limit(x+4,x=0))
plot(x+4,-5,5)
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#2)find the limit as x approaches -2 for y=(x^2+2x+4)/(x+2)
show(limit((x^2+2*x+4)/(x+2),x=-2))
plot((x^2+2*x+4)/(x+2),xmin=-4,xmax=4,ymin=-1000,ymax=1000)
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#3)find the limit as x approaches -2 for y=(x^2+4x+4)/(x+2)
show(limit((x^2+4*x+4)/(x+2),x=-2))
plot((x^2+4*x+4)/(x+2),-5,5)
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factor((x^2+4*x+4)/(x+2))
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((x^2+2*x+4)/(x+2)).simplify_rational()
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#4)
limit(abs(x),x=0)
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plot(abs(x))
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#5)
limit((2*x+1)/(3*x-2),x=infinity)
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plot([(2*x+1)/(3*x-2),2/3],1,1000)
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