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Elements Calculus > Calculus 1 > Flashcards

Calculus 1 Flashcards

1
Q

When f”(x) is negative the curve of y = f(x) is concave

A

A. downward

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2
Q

If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is

A

B. a sinusoid

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3
Q

A function F(x) is called ___of f(x) if F(x) = f(x).

A

D. antiderivative

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4
Q

Points of derivatives which do not exists (and so equals zero) are called

A

D. minimum and maximum

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5
Q

At the minimum point, the slope of the tangent line is

A

D. zero

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6
Q

What is the point where the second derivative is zero?

A

C. Inflection point

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7
Q

The point on the curve where the second derivative of a function is equal to zero is called

A

D. Critical point

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8
Q

The point of the curve where the first derivative of a function is zero and the second derivative is positive is called

A

B. minima

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9
Q

The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz.

A

B. Calculus

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10
Q

The the relation __ of a relation is the set of second elements of the pair in

A

B. Range

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11
Q

A relation in which there is exactly one range element associated with each domain element.

A

D. Function

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12
Q

The relation _ of a relation is the set of first elements of pairs in the

A

A. Domain

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13
Q

Any set of ordered pair is called a

A

A. relation

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14
Q

Any pair of elements (x, y) having a first element x and a second element y is called

A

D. ordered pair

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15
Q

The operation of finding the derivative of function

A

B. Differentiation

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16
Q

The derivative of a function is identical to the __ of the graph of function

A

C. slope

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17
Q

The __ derivative of the function is the rate of change of the slope of the graph

A

B. Second

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18
Q

A point on the graph where the tangent line is either horizontal or vertical is known as

A

B. critical point

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19
Q

The critical points of a graph occur when the derivative of a function is

A

C. zero or approaches infinity

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20
Q

At point of inflection,

A

В. y’’ = 0

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21
Q

At a point where y’ = 0, if y changes from positive to negative as x
increases,

A

C. y is maximum

22
Q

The point where the second derivative of a function is zero.

A

D. Point of inflection

23
Q

The point where the first derivative of a function is zero and the second derivative is positive.

A

B. Minimum point

24
Q

A point at which the curve changes from concave upward to concave downward and vice versa is known as

A

C. point of inflection

25
Q

At a point where y’= 0, if y changes from positive to negative as x increases

A

A. y is maximum

26
Q

is also known as the composite function rule.

A

D. Chain rule

27
Q

The L’Hospital rule was formulated by

A

J. Bernoulli

28
Q

A collective term for maxima or minima, whether absolute of relative is called

A

B. extrema

29
Q

Which of the following is not determinate form?

A

D. ∞/∞

30
Q

Which of the following is determinate?

A

C. ∞.∞

31
Q

Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of

A

C. y = cosh x

32
Q

The quantity 2/(e* -e-*) is equal to

A

C. csch x

33
Q

What is 1 - tan h^2 equal to?

A

A. sec h^2 x

34
Q

In calculus, all functions are classified as either algebraic or transcendental. Which of the following is NOT an algebraic function?

A

D. Exponential logarithmic function

35
Q

The integral of any quotient whose numerator is the difference of the denominator is the _ of the denominator.

A

C. logarithm

36
Q

Many Integrals may be evaluated by introducing a new variable of Integration in place of the original variable, the two variables being connected by some suitable formulas. This process is called

A

B. integration by substitution

37
Q

The variable inside the integral is called variable of integration or integration variable, It is sometimes referred to as

A

B. dummy variable

38
Q

The value of x in trigonometric substitution with an integrand involving (a^2 - x^2) is

A

D. a sin theta

39
Q

The area of the surface generated by rotating any plane curve about a certain axis in its plane id equal to the product of the length of the arc and the distance traveled by its centroid.

A

B. First proposition of Pappus

40
Q

The volume of any solid revolution is equal to the generating are times the circumference of the circle described by the centroid of the area. This is known as

A

C. Second proposition of Pappus

41
Q

Newton was inspired by an apple. Pappus propositions were inspired by what fruits?

A

C. Apple and Lemon

42
Q

When the ellipse is rotated about its longer axis, the ellipsoid is

A

B. prolate

42
Q

When the ellipse is rotated about is shorter axis, the ellipsoid is

A

D. Oblate

42
Q

When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called

A

C. catenoid

43
Q

A solid of revolution of a parabola is known as

A

A. Paraboloid

44
Q

A _ section of a surface of revolution is the section containing the axis of revolution.

A

D. meridian

45
Q

An infinite series in which successive terms are of the form of constant times successive integral power of the variable. It takes the form of ao + a1x + a2x^2 + a3x^3 + ….

A

D. Power series

46
Q

Who invented the symbol for infinity?

A

C. John Wallis

47
Q

Calculus was invented by

A

D. Newton and Leibniz

48
Q

Varignon’s theorem is used to determine

A

A. location of centroid

Elements Calculus (1 decks)

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