3110 Quiz 1 Name: DrSarah Greenwald Start Time: Apr 03, 2000 13:11 Time Allowed: 14 min Number of Questions: 4

Question 1  (10 points)

 1 yes 2 no 3 sometimes, but not always

Question 2  (10 points)

Match the mathematician with their math

 1. Sophie Germain a. Proved the Epsilon Conjecture which says that Taniyama-Shimura implies Fermat's Last Theorem 2. Andrew Wiles b. Worked on the solution of a quintic by radicals 3. Niels Abel c. Proved Fermat's Last Theorem by proving Taniyama-Shimura 4. Ken Ribet d. First mathematician to examine a general approach (for all powers) for Fermat's Last Theorem 5. Lodovico Ferrari e. Worked on the solution of a quartic by radicals
 1 --> Choose Match abcde 2 --> Choose Match abcde 3 --> Choose Match abcde 4 --> Choose Match abcde 5 --> Choose Match abcde

Question 3  (10 points)

Match the the following definitions

 1. f is a function if for all x, there exists y s.t. f(x)=y, and a. for all y, there exists x s.t. f(x)=y 2. f is one-to-one if b. for all x1 and x2, x1=x2 --->f(x1)=f(x2) 3. f is onto if c. for all x1 and x2, f(x1)=f(x2)--->x1=x2
 1 --> Choose Match abc 2 --> Choose Match abc 3 --> Choose Match abc

Question 4  (10 points)

What is the negation of f is continuous at xo ---> (For all E>0, there exists D>0 s.t. |x-xo|<D ---> |f(x)-f(xo)|<E for all x)?

 1 f is continuous at xo and (For all E>0 there exists D>0 s.t. |x-xo|E for all x) 2 f is continuous at xo and (There exists E>0 s.t. for all D>0, there exists x s.t. |x-xo|E) 3 f is continuous at xo and (There exists E>0 s.t. for all D>0, there exists x s.t. |x-xo|>D and |f(x)-f(xo)|>E) 4 f is continuous at xo ---> (There exists E>0 s.t. for all D>0, there exists x s.t. |x-xo| |f(x)-f(xo)|>E) 5 f is continuous at xo ---> (For all E<0, there exits D<0 s.t. |x-xo| |f(x)-f(xo)|>E for all x)