Given that lim x → a f ( x ) = 0 lim x → a g ( x ) = 0 lim x → a h ( x ) = 1 lim x → a p ( x ) = ∞ lim x → a q ( x ) = ∞ which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible. 4. (a) lim x → a [ f ( x ) ] g ( x ) (b) lim x → a [ f ( x ) ] p ( x ) (c) lim x → a [ h ( x ) ] p ( x ) (d) lim x → a [ h ( x ) ] f ( x ) (e) lim x → a [ p ( x ) ] q ( x ) (f) lim x → a p ( x ) q ( x )
Given that lim x → a f ( x ) = 0 lim x → a g ( x ) = 0 lim x → a h ( x ) = 1 lim x → a p ( x ) = ∞ lim x → a q ( x ) = ∞ which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible. 4. (a) lim x → a [ f ( x ) ] g ( x ) (b) lim x → a [ f ( x ) ] p ( x ) (c) lim x → a [ h ( x ) ] p ( x ) (d) lim x → a [ h ( x ) ] f ( x ) (e) lim x → a [ p ( x ) ] q ( x ) (f) lim x → a p ( x ) q ( x )
Solution Summary: The author explains that the limit function undersetxto amathrmlimleft is of the indeterminate form and if not then evaluate the limits.
If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what points c do you automatically know limx-->c ƒ(x)? What can you say about the value of the limit at these points?
Given that
lim x→a f(x) = 0
lim x→a g(x) = 0
lim x→a h(x) = 1
lim x→a p(x) = ∞
lim x→a q(x) = ∞
evaluate if the following limits not are indeterminate forms. (If a limit is indeterminate, enter INDETERMINATE.)
suppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a , except possibly at a. if lim g(x) ,x approaches to a does not exist or lim h(x) ,x approaches to a does not exist , will the lim f(x) ,x approaches to a do or does not exist ?
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