A) A set of integers B) A subset of complex numbers C) A subset of R D) Always the set of all real numbers
A) f(Y) B) fY C) f|Y D) Y(f)
A) Because the text states domains are irrelevant B) Because functions do not require domains C) Because domains are always the entire set of real numbers D) Because it is sometimes possible to enlarge the domain naturally
A) It has no domain B) It depends on r C) It is defined only for x > 0 D) It is everywhere defined
A) If the intersection of their domains contains an open subset of R B) If their domains are identical C) If they are continuous D) If they are both everywhere defined
A) Vector spaces without multiplication B) Groups only C) Commutative algebras over the reals D) Fields
A) Because they lack an additive identity B) Because they are not commutative C) Because addition is not defined D) Because the reciprocal 1/f is not always defined
A) |x + y| B) x - y C) |x - y| D) sqrt(x2 + y2)
A) If the derivative exists at a B) If the limit as x approaches a is infinity C) If f(a) is zero D) If for every ε > 0 there is a δ > 0 such that |f(x) - f(a)| < ε whenever d(x, a) < δ
A) It must be defined everywhere B) It must be continuous at every point of its domain C) It must be differentiable D) It must be a constant function
A) The function must be constant in a neighborhood of a B) For every ε > 0 there exists δ > 0 such that |f(x) - L| < ε for all x in the domain where d(x, a) < δ C) The function must be defined at a D) f(a) must be equal to zero
A) The limit exists if and only if the function is continuous at a B) The limit exists only if the function is differentiable C) The limit always exists D) The limit exists only if the function is constant
A) Extend the domain of f to a by continuity B) Ignore the point a C) Define the derivative at a D) Change the function into a constant function
A) Linear algebra B) Real analysis C) Topology D) Complex analysis
A) A curve B) A matrix C) A scalar D) A domain
A) A parametric equation B) A geometric identity C) A linear projection D) A vector field
A) Integer lattice B) R-vector space C) Boolean algebra D) Finite field
A) Quaternions B) Natural numbers C) Empty set D) Prime numbers
A) No, it is not differentiable B) No, only at positive points C) Yes D) No, only at negative points
A) Only for negative values B) No C) Only for positive values D) Yes
A) Pi + k*pi B) 2*pi + k*pi C) k*pi D) Pi/2 + k*pi
A) Integration by parts B) Implicit differentiation C) Taylor expansion D) Differentiation under the integral sign
A) n B) n+1 C) n-1 D) 1
A) n B) r C) t D) x
A) A matrix of size n by n B) A parametrized n-tuple C) A single real number D) A scalar field |