except -2. Use the definition to justify the example. *5. Suppose f: DR with xo an accumulation point of D. Assume L₁ and L₂ are limits of f at xo. Prove L₁= L2. (Use only the definition; in later theorems, this uniqueness is assumed.) 6. Define f: (0, 1)→ R by f(x) = cos. Does ff have a limit at 0? Justify. 7. Define f: (0, 1)→ R by f(x) = x cos. Does f have a limit at 0? Justify. x³x²+x-1 & Define f: (01)-R by f(x) = Prove that f has a limit at 1
except -2. Use the definition to justify the example. *5. Suppose f: DR with xo an accumulation point of D. Assume L₁ and L₂ are limits of f at xo. Prove L₁= L2. (Use only the definition; in later theorems, this uniqueness is assumed.) 6. Define f: (0, 1)→ R by f(x) = cos. Does ff have a limit at 0? Justify. 7. Define f: (0, 1)→ R by f(x) = x cos. Does f have a limit at 0? Justify. x³x²+x-1 & Define f: (01)-R by f(x) = Prove that f has a limit at 1
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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Questions 5 and 7 please
Transcribed Image Text:except -2. Use the definition to justify the example.
*5. Suppose f: DR with xo an accumulation point of D. Assume L₁ and L₂ are limits of f
at xo. Prove L₁= L2. (Use only the definition; in later theorems, this uniqueness is assumed.)
6. Define f: (0, 1)→ R by f(x) = cos. Does ff have a limit at 0? Justify.
7. Define f: (0, 1)→ R by f(x) = x cos. Does f have a limit at 0? Justify.
x³x²+x-1
& Define f: (01) - R by f(x) =
Prove that f has a limit at 1
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