Question 1028822: I need help with this problem too:
Evaluate the following limit:
The limit of , as x approaches Found 2 solutions by ikleyn, rothauserc:Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website! .
I need help with this problem too:
Evaluate the following limit:
The limit of , as x approaches
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The limit of , as x approaches , is the same as
the limit of , as y approaches .
The last limit equals 1 (one).
It is one of the basic facts of the calculus.
Answer. The limit of , as x approaches , equals 1.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website! limit as x approaches pi of (sin(x-pi)) / (x-pi)
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simplify the expression inside the limit
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(sin(x-pi)) / (x-pi) = sin(x) / (pi-x)
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limit as x approaches pi of sin(x) / (pi-x)
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this intermediate result is of the form 0/0, apply l'Hopital's rule
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limit as x approaches pi of sin(x) / (pi-x) = limit as x approaches pi of (d sin(x)/dx) / d (pi-x)/dx) =
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limit as x approaches pi of cos(x) / -1 =
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limit as x approaches pi of -cos(x)
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substitute pi for x in the expression
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limit as x approaches pi of -cos(x) = -cos(pi) = 1
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