Calculus 1 Flashcards
When f”(x) is negative the curve of y = f(x) is concave
A. downward
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
B. a sinusoid
A function F(x) is called ___of f(x) if F(x) = f(x).
D. antiderivative
Points of derivatives which do not exists (and so equals zero) are called
D. minimum and maximum
At the minimum point, the slope of the tangent line is
D. zero
What is the point where the second derivative is zero?
C. Inflection point
The point on the curve where the second derivative of a function is equal to zero is called
D. Critical point
The point of the curve where the first derivative of a function is zero and the second derivative is positive is called
B. minima
The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz.
B. Calculus
The the relation __ of a relation is the set of second elements of the pair in
B. Range
A relation in which there is exactly one range element associated with each domain element.
D. Function
The relation _ of a relation is the set of first elements of pairs in the
A. Domain
Any set of ordered pair is called a
A. relation
Any pair of elements (x, y) having a first element x and a second element y is called
D. ordered pair
The operation of finding the derivative of function
B. Differentiation
The derivative of a function is identical to the __ of the graph of function
C. slope
The __ derivative of the function is the rate of change of the slope of the graph
B. Second
A point on the graph where the tangent line is either horizontal or vertical is known as
B. critical point
The critical points of a graph occur when the derivative of a function is
C. zero or approaches infinity
At point of inflection,
В. y’’ = 0
At a point where y’ = 0, if y changes from positive to negative as x
increases,
C. y is maximum
The point where the second derivative of a function is zero.
D. Point of inflection
The point where the first derivative of a function is zero and the second derivative is positive.
B. Minimum point
A point at which the curve changes from concave upward to concave downward and vice versa is known as
C. point of inflection
At a point where y’= 0, if y changes from positive to negative as x increases
A. y is maximum
is also known as the composite function rule.
D. Chain rule
The L’Hospital rule was formulated by
J. Bernoulli
A collective term for maxima or minima, whether absolute of relative is called
B. extrema
Which of the following is not determinate form?
D. ∞/∞
Which of the following is determinate?
C. ∞.∞
Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of
C. y = cosh x
The quantity 2/(e* -e-*) is equal to
C. csch x
What is 1 - tan h^2 equal to?
A. sec h^2 x
In calculus, all functions are classified as either algebraic or transcendental. Which of the following is NOT an algebraic function?
D. Exponential logarithmic function
The integral of any quotient whose numerator is the difference of the denominator is the _ of the denominator.
C. logarithm
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
B. integration by substitution
The variable inside the integral is called variable of integration or integration variable, It is sometimes referred to as
B. dummy variable
The value of x in trigonometric substitution with an integrand involving (a^2 - x^2) is
D. a sin theta
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.
B. First proposition of Pappus
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
C. Second proposition of Pappus
Newton was inspired by an apple. Pappus propositions were inspired by what fruits?
C. Apple and Lemon
When the ellipse is rotated about its longer axis, the ellipsoid is
B. prolate
When the ellipse is rotated about is shorter axis, the ellipsoid is
D. Oblate
When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called
C. catenoid
A solid of revolution of a parabola is known as
A. Paraboloid
A _ section of a surface of revolution is the section containing the axis of revolution.
D. meridian
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 + ….
D. Power series
Who invented the symbol for infinity?
C. John Wallis
Calculus was invented by
D. Newton and Leibniz
Varignon’s theorem is used to determine
A. location of centroid
