Read each question carefully. Use complete sentences. Above all
... 2. Why do students need to understand the cancellation property? How would you show them its importance? 3. What role did elliptic curves play in Wiles’ proof of Fermat’s Last Theorem? 4. Show by example that sometimes it is hard to tell whether a number is real. 5. What is Diophantos’ “chord and ta ...
... 2. Why do students need to understand the cancellation property? How would you show them its importance? 3. What role did elliptic curves play in Wiles’ proof of Fermat’s Last Theorem? 4. Show by example that sometimes it is hard to tell whether a number is real. 5. What is Diophantos’ “chord and ta ...
Limits, Sequences, and Hausdorff spaces.
... Definition If (xn ) = x1 , x2 , . . . is a sequence in a Euclidean space Rn , we say that (xn ) converges to x ∈ Rn if for every > 0, we can produce an integer N > 0 such that if n > N , then ||xn − x|| < . That is, eventually the sequence enters and stays within any open ball about the point x. ...
... Definition If (xn ) = x1 , x2 , . . . is a sequence in a Euclidean space Rn , we say that (xn ) converges to x ∈ Rn if for every > 0, we can produce an integer N > 0 such that if n > N , then ||xn − x|| < . That is, eventually the sequence enters and stays within any open ball about the point x. ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.