Calculus 1

Question 1

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

Answer 1

A. downward

Question 2

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

Answer 2

B. a sinusoid

Question 3

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

Answer 3

D. antiderivative

Question 4

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

Answer 4

D. minimum and maximum

Question 5

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

Answer 5

D. zero

Question 6

What is the point where the second derivative is zero?

Answer 6

C. Inflection point

Question 7

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

Answer 7

D. Critical point

Question 8

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

Answer 8

B. minima

Question 9

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

Answer 9

B. Calculus

Question 10

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

Answer 10

B. Range

Question 11

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

Answer 11

D. Function

Question 12

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

Answer 12

A. Domain

Question 13

Any set of ordered pair is called a

Answer 13

A. relation

Question 14

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

Answer 14

D. ordered pair

Question 15

The operation of finding the derivative of function

Answer 15

B. Differentiation

Question 16

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

Answer 16

C. slope

Question 17

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

Answer 17

B. Second

Question 18

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

Answer 18

B. critical point

Question 19

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

Answer 19

C. zero or approaches infinity

Question 20

At point of inflection,

Answer 20

В. y’’ = 0

Question 21

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

Answer 21

C. y is maximum

Question 22

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

Answer 22

D. Point of inflection

Question 23

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

Answer 23

B. Minimum point

Question 24

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

Answer 24

C. point of inflection

Question 25

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

Answer 25

A. y is maximum

Question 26

is also known as the composite function rule.

Answer 26

D. Chain rule

Question 27

The L'Hospital rule was formulated by

Answer 27

J. Bernoulli

Question 28

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

Answer 28

B. extrema

Question 29

Which of the following is not determinate form?

Answer 29

D. ∞/∞

Question 30

Which of the following is determinate?

Answer 30

C. ∞.∞

Question 31

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

Answer 31

C. y = cosh x

Question 32

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

Answer 32

C. csch x

Question 33

What is 1 - tan h^2 equal to?

Answer 33

A. sec h^2 x

Question 34

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

Answer 34

D. Exponential logarithmic function

Question 35

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

Answer 35

C. logarithm

Question 36

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

Answer 36

B. integration by substitution

Question 37

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

Answer 37

B. dummy variable

Question 38

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

Answer 38

D. a sin theta

Question 39

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.

Answer 39

B. First proposition of Pappus

Question 40

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

Answer 40

C. Second proposition of Pappus

Question 41

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

Answer 41

C. Apple and Lemon

Question 42

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

Answer 42

B. prolate

Question 42

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

Answer 42

D. Oblate

Question 42

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

Answer 42

C. catenoid

Question 43

A solid of revolution of a parabola is known as

Answer 43

A. Paraboloid

Question 44

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

Answer 44

D. meridian

Question 45

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 + ....

Answer 45

D. Power series

Question 46

Who invented the symbol for infinity?

Answer 46

C. John Wallis

Question 47

Calculus was invented by

Answer 47

D. Newton and Leibniz

Question 48

Varignon's theorem is used to determine

Answer 48

A. location of centroid