#81AB5
f1(x)=2*x+1
f2(x)=x^2/2+3
f=piecewise([[(-2,2),f1],[(2,5),f2]])
plot(f)
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#76AB7a
var('h')
f(x)=x^2+x
show(lim((f(x+h)-f(x))/h,h=0))
show(lim((f(x+h)-f(x-h))/h,h=0))
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#76AB7b
var('h')
f(x)=cos(x)
show(lim((f(x+h)-f(x))/h,h=0))
show(lim((f(x+h)-f(x-h))/h,h=0))
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