Prove the following using the definition of a limit. a. Given f(x) = 2x – 5, prove that limit lim f(x) = 1. x-3 b. Use the e - 8 definition of the limit to prove that lim = 4. X-2 x-2 -3x c. Suppose that h(x) = Prove that lim h(x) = 3. %3D x-3 x-3

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Prove the following using the definition of a limit.
a. Given f(x) = 2x – 5, prove that limit lim f(x) = 1.
x-3
x2-4
= 4.
b. Use the e - ô definition of the limit to prove that lim
X-2 x-2
x2-3x,
c. Suppose that h(x) = *Prove that lim h(x) = 3.
x-3
X-3
Transcribed Image Text:Prove the following using the definition of a limit. a. Given f(x) = 2x – 5, prove that limit lim f(x) = 1. x-3 x2-4 = 4. b. Use the e - ô definition of the limit to prove that lim X-2 x-2 x2-3x, c. Suppose that h(x) = *Prove that lim h(x) = 3. x-3 X-3
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