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This is a perfect time to use l'Hospital's rule:
If a fraction becomes 0/0 at the limit (like this one does),
then the limit of the fraction is equal to the limit of
(derivative of the numerator)/(derivative of the denominator) .
I'm not sure why l'Hospital's rule stuck with me all these years.
But when it's appropriate, like for this one, you can't beat it.
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Limit as t approches 4 square t minus 2 divided by t-4?
Since both the numerator and the denominator approach zero, the conditions for de l'Hospital's rule are fulfilled. Take the derivate of both the numerator and the denominator, and take the limit of the new fraction: lim (t2-2)/(t-4) = lim 2t / 1 = 8 / 1 = 8.
Limit as x approches -1 of x3 plus x2 plus 3x plus 3 divided by x4 plus x3 plus 2x plus 2?
lim (x3 + x2 + 3x + 3) / (x4 + x3 + 2x + 2)x > -1From the cave of the ancient stone tablets, we cleared away several feet of cobwebs and unearthed"l'Hospital's" rule: If substitution of the limit results in ( 0/0 ), then the limit is equal to the(limit of the derivative of the numerator) divided by (limit of the derivative of the denominator).(3x2 + 2x + 3) / (4x3 + 3x2 + 2) evaluated at (x = -1) is:(3 - 2 + 3) / (-4 + 3 + 2) = 4 / 1 = 1
How do you calculate the limit of e5x -1 divided by sin x as x approaches 0?
You can use the L'hopital's rule to calculate the limit of e5x -1 divided by sin x as x approaches 0.
What is the limit of 2sinx divided by4 as x goes to pi?
0.5
Does the limit exist for fn divided by fn-1 in the Fibonacci sequence and if so what is it?
The limit is the Golden ratio which is 0.5[1 + sqrt(5)]
