Exam (elaborations)
Math 302 Test 3 Questions And Answers Latest Update
- Course
- MATH 302
- Institution
- University Of Southern California
Math 302 Test 3 Questions And Answers Latest Update
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Solution 2024/2025Pepper
Math 302 Test 3 Questions And Answers Latest
Update
What types of functions are continuous? ANS✔✔ Polynomials; rational
functions at points whose denominator is not zero; functions from (some
subset) of R to R
Projection Function ANS✔✔ A function who takes a set of inputs from R^(n)
and projects them down to R is continuous
A function f: E -> R^(n) is continuous iff ANS✔✔ for all 1<= i <= n we have
project(i) composed of f: e->R is continuous
Continuous functions preserve connectedness ANS✔✔ If f:E->E(hat) is
continuous and E is connected, then f(E) is connected as well. Consequence
is that open balls in R^(n) are connected
What properties are preserved under continuous functions? ANS✔✔ Open
under inverse image, closed under inverse image, connected under image,
compactness
What properties are not preserved under continuous functions ANS✔✔ open
under image; closed under image; boundedness
Extreme Value Theorem ANS✔✔ If f: E -> R is continuous and E is compact,
then there exists p₀∈E so that f(p₀) = lub(f(E)). Likewise, there exists p₀l∈E
such that f(p₀l)=glb(f(E))
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