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