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Key Equations

Key Equations

Slope of a Secant Line msec=f(x)−f(a)x−amsec=f(x)−f(a)x−a
Average Velocity over Interval [a,t][a,t] vave=s(t)−s(a)t−avave=s(t)−s(a)t−a
Intuitive Definition of the Limit limx→af(x)=Llimx→af(x)=L
Two Important Limits limx→ax=alimx→ac=climx→ax=alimx→ac=c
One-Sided Limits limx→a−f(x)=Llimx→a+f(x)=Llimx→a−f(x)=Llimx→a+f(x)=L
Infinite Limits from the Left limx→a−f(x)=+∞limx→a−f(x)=−∞limx→a−f(x)=+∞limx→a−f(x)=−∞
Infinite Limits from the Right limx→a+f(x)=+∞limx→a+f(x)=−∞limx→a+f(x)=+∞limx→a+f(x)=−∞
Two-Sided Infinite Limits limx→af(x)=+∞:limx→a−f(x)=+∞limx→af(x)=+∞:limx→a−f(x)=+∞ and limx→a+f(x)=+∞limx→a+f(x)=+∞
 limx→af(x)=−∞:limx→a−f(x)=−∞limx→af(x)=−∞:limx→a−f(x)=−∞ and limx→a+f(x)=−∞limx→a+f(x)=−∞
Basic Limit Results limx→ax=alimx→ac=climx→ax=alimx→ac=c
Important Limits limθ→0sinθ=0limθ→0sinθ=0
 limθ→0cosθ=1limθ→0cosθ=1
 limθ→0sinθθ=1limθ→0sinθθ=1
 limθ→01−cosθθ=0limθ→01−cosθθ=0