Calculus Volume 1

Key Equations

Calculus Volume 1Key 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 $limθ→0sinθ=0limθ→0sinθ=0$ $limθ→0cosθ=1limθ→0cosθ=1$ $limθ→0sinθθ=1limθ→0sinθθ=1$ $limθ→01−cosθθ=0limθ→01−cosθθ=0$
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