REM A LEVEL 1, 2, & 3 Flashcards
What is/are the conditions for a
function to be continuous on (a,b)?
i. The function is continuous at each
point of (a,b)
ii. The function is right continuous
iii. The function is left continuous
A. i only
B. i and ii
C. i and ii
D. i, ii, and ii
E. i and ii
D. i, ii, and ii
The function y=(x-4)/(x+2) is
discontinuous at x equals?
A. 12
B. 2
C. 0
D. -2
D. -2
The given function will have a vertical
asymptote at x =-2. Therefore, the
function is discontinuous at x =-2.
A function is invertible if it is
A. Injective
B. Surjective
C. Bijective
D. Surjective
C. Bijective
At the maximum point, the second
derivative of the curve is
A. 0
B. Negative
C. Positive
D. 1
B. Negative
A curve y = f(x) is concave downward if
the value of y” is
A. zero
B. positive
C. negative
C. negative
At the point of inflection, if y=f(x) is
concaving downward, then y” is
negative. If y=f(x) is concaving upward,
then y” is positive.
The partial derivative expression f_xx(x,
y) means
A. a^2y/af^2
B. a^2x/af^2
C. a^2f/ax^2
D. a^2y/af^2
E. a^2f/ay^2
C. a^2f/ax^2
The partial derivative expression f_x(x,y)
means
A. ay/af
B. af/ax
C. ax/af
D. af/ay
B. af/ax
A curve produced by tracing the path of a chosen point on the circumference of a circle which rolls without slipping around a fixed circle.
A. Hypotrochoid
B. Epicycloid
C. Epitrochoid
D. Hypocyloid
B. Epicycloid
The theorem that is defined by:
(REM A L1,2,3 FIGURE)
A. The Integral Prime theorem
B. The Difference theorem
C. The Net Change theorem
C. The Net Change theorem
It is a differential equation that can be
written as dy/dx=F(x)G(y) in which the
derivative equals a product of a function
just of x and a function just of y.
A. Homogeneous DE
B. Exact DE
C. Variable Separable DE
C. Variable Separable DE
(REM A L1,2,3 FIGURE)
Condition for exactness for differential
equation Mdx+Ndy=0 is
A. aM/ay = aN/ax
B. aM/ax = an/ay
C. M = N
D. Mdx = -Ndy
A. aM/ay = aN/ax
A solution which can’t be obtained from
a general solution is called _____ solution
A. Singular
B. None of these choices
C. Particular
A. Singular
A solution is called the singular solution of the differential equation F(x, y, y)=0 if it cannot be obtained from the general solution for any choice of arbitrary constant c, including infinity. In other words, if the initial value problem has at least two solutions, then those of which that is not a member of the general solution is called singular.
Laplace transform of the output
response of a linear system is the
system transfer function when the input
is
A. Ramp Signal
B. Impulse Signal
C. Step Signal
B. Impulse Signal
If the input is impulse signal, then the
output is 1. Thus, the Laplace transform
of the output response of a linear
system is equal to the transfer function
Denote òu be the partial derivative of a
function u. Given the linear second-
order partial differential equation.Where A, B, C, D, E and F are real constants. If B-4AC< 0, the above equation is:
(REM A L1,2,3 FIGURE)
A. Asymptotic
B. Hyperbolic
C. Elliptic
D. Parabolic
C. Elliptic
If B^2 - 4AC = 0, it is parabolic
If B^2 - 4AC< 0, it is elliptic
If B^2 - 4AC > 0, it is hyperbolic
A fractional integral of order 1/2.
A. Inverse integral
B. Anti integral
C. Sub integral
B. Anti integral
A curve generated by the trace of a fixed point on a small circle that rolls withn a large circle.
A. Epitrochoid
B. Epicycloid
C. Hypocycloid
D. Hypotrochoid
C. Hypocycloid
Determine the type of the given
Differential Equation: dy/dx + 3xy = xy^2
A. Bernoulli’s DE
B. Homogeneous DE
C. Linear DE
D. Variable Separable DE
A. Bernoulli’s DE
The equation
(REM A L1,2,3 FIGURE)
A. Heat Equation
B. Wave Equation
C. Oscillation Equation
D. Heat Equation
B. Wave Equation
Denote òu be the partial derivative of a
function u. Given the linear second-
order partial differential equation
(REM A L1,2,3 GIGURE)
Where A, B, C, D, E and F are real constants.
If B²-4AC> 0, the above equation is
A. Hyperbolic
B. Parabolic
C. Asymptotic
D. Elliptic
A. Hyperbolic
If B-4AC> 0, the PDE is hyperbolic.
If B-4AC< 0, the PDE is elliptic.
If B-4AC= 0, the PDE is parabolic.
In Advanced Mathematics, it is an
integral transform that converts a
function of a real variable t to a complex
variable s.
A. Laplace Transform
B. Fourier Transform
C. Borel Transform
D. Fourier Transform
A. Laplace Transform
What is the domain of a function?
A. the maximal set of numbers for which a
function is defined
B. the maximal set of numbers which a
function can take values
C. it is a set of natural numbers for which a
function is defined
A. the maximal set of numbers for which a
function is defined
If A and B are constants, the secondorder differential equation xy”+ Axy’+By = 0 is called _____
A. Bernoulli’s DE
B. Riccati DE
C. Euler’s DE
C. Euler’s DE
Determine the differential equation of the family of lines passing through the origin.
A. xdy - ydx = 0
B. xdx - ydy = 0
C. xdx + ydy = 0
D. xdy + ydx = 0
A. xdy - ydx = 0
Let the equation of lines be y = mx, where m is a slope
Differentiating the equation: dy/dx = m, m = y/x
Thus, dy/dx = y/x - xdy-ydx = 0
The kernel of Laplace Transform is:
A. e^(-st)
B. z^(-n)
C. e^(-jw)
D. e^(-n)
A. e^(-st)
