Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L (a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x lim ck() L. = L and (b) Define a new function: тЕО l(x) = \g(x), otherwise. Prove that limcl(x) = L. Hint: Use part (a) and the squeeze theorem. (c) Conclude that for the function: хеQ 0, otherwise F(x) = we have lim+0 F(x) = 0.
Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L (a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x lim ck() L. = L and (b) Define a new function: тЕО l(x) = \g(x), otherwise. Prove that limcl(x) = L. Hint: Use part (a) and the squeeze theorem. (c) Conclude that for the function: хеQ 0, otherwise F(x) = we have lim+0 F(x) = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L
(a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x
lim ck() L.
= L and
(b) Define a new function:
тЕО
l(x) =
\g(x), otherwise.
Prove that limcl(x) = L.
Hint: Use part (a) and the squeeze theorem.
(c) Conclude that for the function:
хеQ
0, otherwise
F(x) =
we have lim+0 F(x) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff121ba60-7058-4a7c-893c-99f8ff2d6afa%2F45c39167-f90e-4f2e-aca5-38ad586ee19a%2Feqdkhg9.png&w=3840&q=75)
Transcribed Image Text:Exercise 2: Hard] Let f,g be functions such that limc f(x) = L and lim,c g(x) = L
(a) Let h(x) max{f(x),g(x)}, and let k(x) min{f(x), g(x)}. Prove that limc h(x
lim ck() L.
= L and
(b) Define a new function:
тЕО
l(x) =
\g(x), otherwise.
Prove that limcl(x) = L.
Hint: Use part (a) and the squeeze theorem.
(c) Conclude that for the function:
хеQ
0, otherwise
F(x) =
we have lim+0 F(x) = 0.
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