Calculus 7.5-7.9. 7.5 Indeterminant Forms L’Hopital’s Rule If f(a)=g(a)=0,
L’Hopital’s Rule Limits of the form correspond to undetermined forms of limits since the result...
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Transcript of L’Hopital’s Rule Limits of the form correspond to undetermined forms of limits since the result...
L’Hopital’s Rule
Limits of the form correspond to undetermined forms of limits since the result
depends upon the expression in consideration. L’Hopital’s rule tells how to deal with this type
of limits using derivatives
Exercise
Determine whether the following limits are of the form or neither
Limits of the form
Evaluate the following limits
Using the Tangent Lines
f(x)
Tangent line to f(x) at x=1
g(x)Tangent line to g(x) at x=1
Using the Tangent Lines
Tangent line to g(x) at x=1
f(x)Tangent line to f(x) at x=1
g(x)
First Version of L’Hopital’s Rule
The limit at x=1 is the same as the quotient of the derivatives at x=1
L’Hopital’s Rule
In a simpler language it says that to calculate the limit of the quotient of two functions at a point a, where the limit is of the form " 0”/" 0” , it is the same as the limit of the quotient of their derivatives at that point.
L'Hopital's rule also holds if we replace the limiting point a for ∞, -∞, a+, a-
Practice
Calculate the following limits. In case you want to use L’Hopital’s rule verify that the conditions are satisfied.
1.
2.
3.