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1.5.10 Limits




  • Here is the expression


    .
  • In[1]:= t = Sin[x]/x

    Out[1]=

  • If you replace x by 0, the expression becomes 0/0, and you get an indeterminate result.
  • In[2]:= t /. x->0

    1
    Power::infy: Infinite expression - encountered.
    0

    Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered.

    Out[2]=













  • If you find the numerical value of for close to , however, you get a result that is close to


    .
  • In[3]:= t /. x->0.01

    Out[3]=













  • This finds the limit of as approaches . The result is indeed


    .
  • In[4]:= Limit[t, x->0]

    Out[4]=


    Limits.