Differential and Integral Calculus Terms and Elements - ME Boards Exam

The derivative of aᵘ with respect to x is... A. aᵘ ln a (du/dx) B. aᵘ ln u (du/dx) C. uᵃ ln a (du/dx) D. uᵃ ln u (du/dx)

A. aᵘ ln a (du/dx)

The ____________ of a relation is the set of first elements of pairs in the relation. A. domain B. range C. graph D. function

A. domain

When f"(x) is negative the curve of y = f(x) is concave ____________. A. downward B. to the right C. upward D. to the left

A. downward

Varignon's theorem is used to determine... A. location of centroid B. moment of inertia C. mass moment of inertia D, moment of area

A. location of centroid

A solid of revolution of a parabola is known as... A. paraboloid B. hyperboloid C. catenoid D. conoid

A. paraboloid

Any set of ordered pair is called a... A. relation B. range C. domain D. graph

A. relation

What is 1 - tan h² x equal to? A. sec h² x B. cos h² x C. cot h² x D. csc h² x

A. sec h² x

If y = tanh x, find dy/dx A. sech² x B. -sech² x C. sech x tanh x D. -sech x tanh x

A. sech² x

At a point where y' = 0, if y changes from positive to negative as x increases... A. y is maximum B. y is minimum C. x is maximum D. y is minimum

A. y is maximum

The integral of sin cos" o do can easily be determined by using Wallis formula provided the limits are form. A. 0 to π B. 0 to π/2 C. 0 to π/4 D. 0 to 2π

B. 0 to π/2

The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz. A. Physics B. Calculus C. Boolean Algebra D. Quantum Mechanics

B. Calculus

The operation of finding the derivative of a function. A. Differentiating B. Differentiation C. Differential D. Integrating

B. Differentiation

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. Varignon's theorem B. First proposition of Pappus C. Method of section D. Second proposition of Pappus

B. First proposition of Pappus

Evaluate the integral of tanh u du. A. In sinh u + C B. In cos hu + C C. cosh u + C D. coth u + C

B. In cos hu + C

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. Integration by parts B. Integration by substitution C. partial derivatives D. the chain rule

B. Integration by substitution

The point where the first derivative of a function is zero and the second derivative is a positive. A. Minimum point B. Maximum point C. Point of Inflection D. Critical point

B. Maximum point

If the second derivative of negative of the equation of a curve is equal to the equation of that same curve, the curve is... A. a paraboloid B. a sinusoid C. a cissoid D. an exponential

B. a sinusoid

A point on the graph where the tangent line is either horizontal or vertical is known as... A. point of inflection B. critical point C. stationary point D. all of the above

B. critical point

The variable inside the integral is called variable of integration or integration variable. It is sometimes referred to as... A. calculus variable B. dummy variable C. limits variable D. limits range

B. dummy variable

A collective term for maxima or minima, whether absolute of relative is called... A. infinitium B. extrema C. domain D. none of the above

B. extrema

At the point of inflection where x = a... A. f"(a) ≠ 0 B. f(a) = 0 C. f(a) > 0 D. f"(a) < 0

B. f(a) = 0

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

B. minima

When the ellipse is rotated about its longer axis, the ellipsoid is... A. paraboloid B. prolate C. spheroid D. oblate

B. prolate

The ______________ of a relation is the set of second elements of the pair in the relation. A. domain B. range C. graph D. function

B. range

The ___________ derivative of the function is the rate of change of the slope of the graph. A. first B. second C. third D. fourth

B. second

At point of inflection... A. y'= 0 B. y" = 0 C. y" is negative D. y" is positive

B. y" = 0

The derivative of csc Θ is... A. sec Θ tan Θ B. -csc² Θ C. -csc Θ cot Θ D. -csc Θ tan Θ

C. -csc Θ cot Θ

Newton was inspired by an apple. Pappus propositions were inspired by what fruits? A. Apple and pear B. Lemon and orange C. Apple and lemon D. Apple and banana

C. Apple and lemon

What is the point where the second derivative is zero? A. Maxima B. Minima C. Inflection point D. Point of intersection

C. Inflection point

The L'Hospital rule was formulated by... A. Marquis de l'Hospital B. Marrione de l'Hospital C. J. Bernoulli D. I. Newton

C. J. Bernoulli

Who invented the symbol "∞" for infinity? A. John Stockton B. John Venn C. John Wallis D. John Napier

C. John Wallis

The volume of any solid revolution is equal to the generating area times the circumference of the circle described by the centroid of the area. This is known as... A. First proposition of Pappus B. Cavalieri's theorem C. Second proposition of Pappus D. Simpson's Rule

C. Second proposition of Pappus

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

C. Zero or approaches infinity

When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called... A. paraboloid B. hyperboloid C. catenoid D. conoid

C. catenoid

The quantity 2/(Θ^x - Θ^-x) is equal to... A. cosh x B. tanh x C. csch x D. sech x

C. csch x

The integral of any quotient whose numerator is the difference of the denominator is the _____________ of the denominator. A. reciprocal B. product C. logarithm D. derivative

C. logarithm

A point at which the curve changes from concave upward to concave downward and vice versa is known as... A. point of intersection B. point of deflection C. point of inflection D. yield point

C. point of inflection

The derivative of a function is identical to the ____________ of the graph of the function. A. tangent B. secant C. slope D. normal

C. slope

Catenary is the shape assumed by perfectly flexible uniform cable hanging between supports. It is a graph of... A. parabola B. y = sinh x C. y = cosh x D. x = cosh y

C. y = cosh x

At a point where y' = 0, if y changes from positive to negative as x increases... A. y is minimum B. x is minimum C. y is maximum D. x is maximum

C. y is maximum

Which of the following is determinate? A. 0/0 B. 0 x ∞ C. ∞ x ∞ D. ∞^0

C. ∞ x ∞

_____________ is also known as the composite function rule. A. L'Hospital rule B. Trapezoidal rule C. Simpson's rule D. Chain rule

D. Chain rule

In calculus, all functions are classified as either algebraic or transcendental. Which of the following is NOT an algebraic function? A. Rational integral function B. Irrational function C. Rational fractional function D. Exponential logarithmic function

D. Exponential logarithmic function

A relation in which there is exactly one range element associated with each domain element. A. Graph B. Set C. Formula D. Function

D. Function

Calculus was invented by... A. Newton B. Leibniz C. Gauss D. Newton and Leibniz

D. Newton and Leibniz

The point where the second derivative of a function is zero. A. Maximum point B. Minimum point C. Point of intersection D. Point of inflection

D. Point of inflection

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 a₀ + a₁ x + a₂ x² + a₃ x³ + ... A. Fourier series B. Taylor's series C. McClaurin series D. Power series

D. Power series

The value of x in trigonometric substitution with an integral involving (a²-x²) is... A. a sec Θ B. a tan Θ C. a cos Θ D. a sin Θ

D. a sin Θ

At maximum point... A. the curve is concave downward B. y" is negative C. y' = 0 D. all of the above

D. all of the above

A function F(x) is called ____________ of f(x) if F'(x) = f(x). A. explicit function B. derivative C. implicit function D. antiderivative

D. antiderivative

The point on the curve where the second derivative of a function is equal to zero is called... A. maxima B. minima C. point of inflection D. critical point

D. critical point

A _________________ section of a surface of revolution is the section containing the axis of revolution. A. right B. central C. median D. meridian

D. meridian

Points of derivatives which do not exists (and so equals zero) are called ______________. A. stationary points B. minimum points C. maximum points D. minimum and maximum

D. minimum and maximum

When the ellipse is rotated about its shorter axis, the ellipsoid is... A. paraboloid B. prolate C. spheroid D. oblate

D. oblate

Any pair of elements (x, y) having a first element x and a second element y is called... A. range B. domain C. coordinates D. ordered pair

D. ordered pair

At the minimum point, the slope of the tangent line is... A. negative B. infinity C. positive D. zero

D. zero

Which of the following is not determinate form? A. ∞ x ∞ B. ∞ + ∞ C. -∞ - ∞ D. ∞/∞

D. ∞/∞