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Differential & Integral Calculus Terms Flashcards | StudBud
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Differential & Integral Calculus Terms
Differential & Integral Calculus Terms
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1
When f(x) is negative the curve of y = f(x) Is concave _______
D. to the left
A. downward
C. upward
B. to the right
2
What is 1 - tan h2 x equal to?
A. sec h2 x
D. csc h2 x
B. cos h2 x
C. cot h2x
3
The point on the curve where the second derivative of a function is equal to zero is called
A. maxima
B. minima
D. critical point
C. point of inflection
4
A relation in which there is exactly one range element associated with each domain element,
A. Graph
C Formula
D Function
B. Set
5
If y = tanhx, find dy/dx.
A. sech2 x
B. -sech2x
C. sech x tanh x
D. -sech x tanh x
6
Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of
D. x = cosh Y
A. parabola
B. y = sinh x
C. Y = cosh x
7
A collective term for maxima or minima, whether absolute of relative is called
D. none of the above
A. infinitium
C. domain
B. extrema
8
Which of the following is not determinate form?
C. -∞-∞
B. ∞+∞
D. ∞/∞
A. ∞ (∞)
9
An infinite series in which successive terms are of the form of constant times successive integral power of the variabl
D. Power series
B. Taylor's series
C. McClaurin series
A. Fourier series
10
If second derivative of the equation of a curve is equal to negative of the equation of that same curve, the curve is
B. a sinusoid
D. an exponential
A. a paraboloid
C. a cissoid
11
The area of the surface generated by rotating any plane curve about a certain axis in its plane is equal to the product
B. First proposition of Pappus
A. Varignon’s theorem
D. Second proposition of Pappus
C. Method of section
12
The volume of any solid revolution is equal to the generating are times the circumference of the circle described by the
D. Simpson's Rule
B. Cavalieri's theorem
A. First proposition of Pappus
C. Second proposition of Pappus
13
The L'Hospital rule was formulated by
D. l. Newton
A. Marquis de. l'Hospital
C. J. Bernoulli
B. Marrlone de l'HospltaI
14
In cal, all functions are classified as either algebraic/transcendental.Which of the ff. is NOT an algebraic function?
B. Irrational function
D. Exponential logarithmic function
C. Rational fractional function
A. Rational integral function
15
The derivative of au with respect to x is
C. ua In(a) du/dx
D. ua In(u) du/dx
A. au In(a) du/dx
B. au In(u) du/dx
16
The _______ of a relation is the set of second elements of the pair in the relation.
D. function
A. domain
C. graph
B. range
17
The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton end Leibniz.
D. Quantum Mechanics
B, Calculus
A. Physics
C. Boolean Algebra
18
At the minimum point, the slope of the tangent line is
C. positive
D. zero
A. negative
B. infinity
19
What is the point where the second derivative is zero?
C. Inflection point
A. Maxima
B. Minima
D. Point of intersection
20
When the ellipse is rotated about is shorter axis, the ellipsoid is
C. spheroid
B. prolate
A. paraboloid
D. oblate
21
Who invented the symbol “∞”for infinity?
D. John Napier
B. John Venn
A. John Stockton
C. John Wallis
22
The derivative of a function is identical to the _____ of the graph of the function.
C. slope
B. secant
A. tangent
D. normal
23
Variable inside the integral is called variable of integration or integration variable, It is sometimes referred to as
C. limits variable
D. limits range
B. dummy variable
A. calculus variable
24
The _______derivative of the function is the rate of change of the slope of the graph.
B. second
C. third
A. first
D. fourth
25
Calculus was invented by
C. Gauss
D. Newton and Leibniz
A. Newton
B. Leibniz
26
The point of the curve where the first derivative of a function is zero and the second derivative is positive is called
A. maxima
B. minima
C. point of inflection
D. critical point
27
Varignon's theorem Is used to determine
B. moment of inertia
D. moment of area
A. location of centroid
C. mass moment of inertia
28
A function F(x) is called ______ of f(x) if F'(x) = f(x).
C. implicit function
A. explicit function
B. derivative
D. antiderivative
29
The integral of sinm α cosn α dα can easily be determined by using
A. 0 to π
D. 0 to 2 π
B. 0 to π/2
C. 0 to π/4
30
The ____ of a relation is the set of first elements of pairs in the relation
B. range
A. domain
D. function
C. graph
31
______ section of a surface of revolution is the section containing the axis of revolution
D. meridian
B. central
C. median
A. right
32
The quantity 2/(ex – e-x) is equal to
A. cosh x
C. csch x
B. tanh x
D. sech x
33
When the ellipse is rotated about its longer axis, the ellipsoid is
C. spheroid
B. prolate
D. oblate
A. paraboloid
34
_______ is also known as the composite function rule.
A. L'Hospital rule
C. Simpson's rule
B. Trapezoidal rule
D. Chain rule
35
At a point where y' = 0. if y changes from positive to negative as x increases.
D. x is maximum
A. y is minimum
C. y is maximum
B. x is minimum
36
At a point where y' = 0. If y changes from positive to negative as x increases
A. y is maximum
D. y is minimum
C. x is maximum
B. y is minimum
37
The operation of finding the derivative of a function.
B. Differentiation
A. Differentiating
C. Differential
D. Integrating
38
A point at which the curve changes from concave upward to concave downward and vice versa Is known as
C. point of inflection
A. point of intersection
B. point of deflection
D. yield point
39
The point where the first derivative of ä function is zero and the second derivative is positive.
C. Point of Inflection
B. Minimum point
D. Critical point
A. Maximum point
40
A solid of revolution of a parabola is known as
A. paraboloid
D. conoid
B. hyperboloid
C. catenoid
41
Many Integrals may be evaluated by introducing a new variable of integration in place of the original variable, the two
D. the chain rule
C. partial derivatives
A. integration by parts
B. Integration by substitution
42
The integral of any quotient whose numerator is the difference of the denominator is the ___of the denominator.
D. derivative
A. reciprocal
C. logarithm
B. product
43
At point of inflection
C. y" is negative
D. y" is positive
B. y” = 0
A. y’ = 0
44
The value of x in trigonometric substitution with an integrand involving (a2 - x 2) is
D. a sin σ
A. a sec σ
B. a tan σ
C. a cos σ
45
A point on the graph where the tangent line is either horizontal or vertical is known as
D. all of the above
A. point of Inflection
C. stationary point
B. critical point
46
At the point of inflection where x = a,
C. f ”(a) > 0
B. f ”(a) = 0
A. f ”(a) not equal 0
D. f ”(a) < 0
47
Any set of ordered pair is called a
B. range
A. relation
D. graph
C. domain
48
The derivative of csc α is
C. -csc α cot α
D. -csc α tan α
B. -csc2 α
A. see α tan α
49
When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called
D. hyperboloid
A. paraboloid
B. conoid
C. catenoid
50
At maximum point,
A. the curve is concave downward
B. y” Is negative
C. y’ = 0
D. all of the above
51
Points of derivatives which do not exists (and so equals zero) are called ________
D. minimum and maximum points
A. stationary points
B. minimum points
C. maximum points
52
The critical points of a graph occur when the derivative of a function is
A. zero
B. approaches Infinity
C. zero or approaches infinity
D, either 1 or -1
53
Evaluate the integral of tanh u du.
C. cosh u + c
A. In sinh u + c
D. coth u + c
B. In cos h u + c
54
Any pair of elements (x, y) having a first element x and a second element y is called
C. coordinates
D. ordered pair
A. range
B. domain
55
The point where the second derivative of a function is zero.
D. Point of inflection
C. Point of intersection
A. Maximum point
B. Minimum point
56
Newton was inspired by an apple. Pappus propositions were inspired by what fruits?
C. Apple and Lemon
A. Apple and pear
B. Lemon and orange
D. Apple and banana
57
Which of the following is determinate?
D. ∞0
C. ∞(∞)
A. 0/0
B. 0(∞)
