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DE/CAL
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1
At point of inflection.
y" is positive
y'=0
y"=0
y" is negative
2
The operation of finding the derivative of a function.
differential
differrentiation
differentiating
integrating
3
The critical points of a graph occur when the derivative of a function is
either 1 or -1
zero
zero and approaches to infinity
approaches to infinity
4
section of a surface of revolution is the section containing the axis of revolution.
right
meridian
median
central
5
derivative of the function is the rate of change of the slope of the graph
second
fourth
third
first
6
Many Integrals may be evaluated by introducing a new variable of Integration in place of the original variable, the two
integration by parts
partial derivatives
integration by substitution
the chain rule
7
When the ellipse is rotated about its longer axis, the ellipsoid is
oblate
spheroid
paraboloid
prolate
8
A relation in which there is exactly one range element associatedwith each domain element
graph
set
formula
function
9
of f(x) if (x) = f(x)
implicit function
derivative
antiderivative
explicit function
10
The derivative of a function is identical to the____ of the graph of the function
normal
slope
tangent
secant
11
The point of the curve where the first derivative of a function is zero and the second derivative is positive is called
critical points
maxima
minima
point of inflection
12
In calculus, all functions are classified as either algebraic or transcendental. Which of the following is NOT an algebr
Rational integral function
Rational fractional function
Exponential logarithmic function
Irrational function
13
The Integral of sin" e cos" e de can easily be determined by using Wallis formula provided the limits are form
0 to pi
0 to π/2
0 to 2pi
0 to π/4
14
At the minimum point, the slope of the tangent line is
positive
infinity
negative
zero
15
Any set of ordered pair is called a
range
domain
relation
graph
16
Vangnon's theorem is used to determine
moment of inertia
moment of area
location of centroid
mass moment of inertia
17
The L'Hospital rule was formulated by
Marrione de Hospital
Marquis de Hospital
J. bernoulli
I. newton
18
What is 1-lan h' x equal to?
sech² x
csc h² x
cos h²x
cot h² x
19
At a point where y= 0, if y changes from positive to negative increases
x is minimum
x is maximum
y is maximum
y is maximum
20
Any pair of elements (x, y) having a first element x and a second element y is called
ordered pair
range
domain
coordinates
21
A collective term for maxima or minima, whether absolute of relative is cated
domain
maxima
infinitium
all of the above
22
if the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the cur
exponential
paraboloid
a cissoid
sinusoid
23
When a catenary (y cosh x) is rotated about its axis of symmetry, it generates a solid called
catenoid
conoid
hyperboloid
paraboloid
24
At maximum point,
y'' is 0
y'' is negative
the curve is concave downward
All of the above
25
Calculus was invented by
Newton
Gauss
Leibniz
Newton and Leibniz
26
At a point where y = 0 if y changes from positive to negative as x increases
x is maximum
x is minimun
y is maximum
y is minimum
27
The derivative of a" with respect to x is
u^a ln u du/dx
a^u ln a du/dx
u^a ln a du/dx
a^u ln u du/dx
28
An infinite series in which successive terms are of the form of constant times successive integral power of the variable
Taylor's series
Power series
McClaurin series
Fourier series
29
Which of the following is determinate?
infinity raised to 0
0, infinity
infinity, infinity
0/0
30
The integral of any quotient whose numerator is the difference of the denominator is the ________of the denominator
logarithm
reciprocal
product
derivative
31
Newton was inspired by an apple. Pappus propositions were inspired by what fruits?
Lemon and orange
Apple and Lemon
Apple and pear
Apple and banana
32
The value of x in trigonometric substitution with an integrand involving (a² - x²) is
a sec theta
a sec theta
a sin theta
a cos theta
33
When the ellipse is rotated about is shorter axis , the ellipsoid is
prolate
paraboloid
oblate
spheroid
34
Who invented the symbol for infinity?
John Napier
John Wallis
John Venn
John Stockton
35
A point at which the curve changes from concave upward to concave
yield point
point of deflection
point of inflection
point of intersection
36
If y=tanhx, find dy/dx.
sech x tanh x
A sech² x
-sech x tanh x
-sech²x
37
The______of a relation is the set of first elements of pairs in therelation
function
range
domain
graph
38
A point on the graph where the tangent line is either horizontal or vertical is known as
all of the above
critical point
stationary point
point of inflection
39
The quantity 2/(e^x-e^x) is equal to
sech x
csch x
tinh x
cosh x
40
The point where the first derivative of a function is zero and the second derivative is positive
point of intersection
maximum point
minimum point
point of inflection
41
The point where the second derivative of a function is zero
maximum point
minimum point
point of inflection
point of intersection
42
The point on the curve where the second derivative of a function is equal to zero is called
point of inflection
minima
maxima
Critical points
43
is also known as the composite function rule
Chain rule
Trapezoidal rule
L'Hospital rule
Simpson's rule
44
Evaluate the integral of tanh u du
coth u + c
In cos hu+c
cosh u + c
ln sinh u + c
45
The volume of any solid revolution is equal to the generating are times the circumference of the circle describe
Second proposition of Pappus
Cavalier's theorem
Simpson's Rule
First proposition of Pappus
46
The of a relation is the set of second elements of the pair in the relation
function
graph
range
domain
47
The variable inside the integral is called variable of integration or integration variable. It is sometimes referred to
dummy variable
calculus variable
limits range
limits variable
48
The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz
Boolean Algebra
quantum mechanics
physics
calculus
49
Which of the following is not determinate form?
infinity + infinity
infinity/infinity
Infinity, infinity
- infinity, - infinity
50
The area of the surface generated by rotating any plane curve about a certain axis in its plane id equal to the product
Second proposition of Pappus
Varignon's theoremn
First proposition of Pappus
Method of section
51
What is the point where the second derivative is zero?
inflection point
minima
maxima
point of intersectio
52
When F(x) is negative the curve of y f(x) is concave
upward
Downward
to the left
to the right
53
Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of
x = cosh y
y=sinh x
parabola
y = cosh x
