anonymous
  • anonymous
f(x)=tan(x) Find the limit as x approaches pi/2 from the negative and positive sides then find the limit as x approaches 0. Help please!! :(
MIT 18.01 Single Variable Calculus (OCW)
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anonymous
  • anonymous
f(x)=tan(x) Find the limit as x approaches pi/2 from the negative and positive sides then find the limit as x approaches 0. Help please!! :(
MIT 18.01 Single Variable Calculus (OCW)
chestercat
  • chestercat
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anonymous
  • anonymous
i think if you make a graphic you can solve the problem more easy , substitute the values of x and make the graphic.
anonymous
  • anonymous
Here how you can proceed,tanx at the positive side of pi/2 (right hand) takes nonpositive values and at the left side it takes nonnegative values now for limit to exist limit from tight and left must exist and be equal to each other so only possible choice in this case is both to be 0 however as one approaches to pi/2 sinx increase and cosx decreases leading to tanx become larger over any bounds so at left side tangent goes to infinity on the posive side and at right limit tangent goes to inifinity at the negative side so limit does not exist
anonymous
  • anonymous
\[\tan x=\sin x/\cos x\]\[\cos (pi/2) = 0\] so as tan x approaches \[pi/2\] from right or left it goes to infinity as cos x gets smaller and smaller.

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anonymous
  • anonymous
look at the graph of tanx.... and see where does it tends when it is approaching pi/2... so it is infinity...from both sides...!!!

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