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Direct Substitution Th. Limf(x)=f(a) Theorem 2 If f(x)<g(x), then limf(x)<limg(x) Squeeze Theorem If f(x)<g(x)<h(x) limf(x)=limh(x)=L, then limg(x)=L Eps - Delta Definition if 0<|x-a|<d, then |f(x)-L|<Eps. Deffinition fuction is cont. if limf(x)=f(a) Theorem 5 Any polinomial and rational functions are cont. Theorem 7 Any pol, ration, root, trig, invers, exponent, and log functions are continuous. Theorem 8 limf(g(x))=f(limg(x)) Intermidiate Value Theorem If f is cont. [a,b] and N is between f(a) & f(b), then there is a C between a & b, such that f(C)=N Deriviative f'(a)=lim(h->0):{f(a+h)-f(a)}/h Rate of change R=lim(x2->x1):{f(x2)-f(x1)}/x2-x1
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L'Hospitals rule states that for a function f(x) = g(x)/h(x) if the limit of g'(x)/h'(x) exists and is equal to a value, then the lmit of f(x) is also equal to that value.
A,e,f,g,h,i,k,l,m,n,t,v,w,x,y,z .... but capitalized.
A,e,f,g,h,i,k,l,m,n,t,v,w,x,y,z .... but capitalized.