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 function F(x) is called ____ of f(x) if F'(x) = f(x)

Points of derivatives which do no exists (and so equals zero) are called ____

At the point of inflection where x = a

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

What is the point where the second derivative is zero?

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

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

Evaluate the integral of tanh u du

The derivative of a^u with respect to x is

If y = tanh x, find dy/dx

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

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

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

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

Any set of ordered pair is called a

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

The operation of finding the derivative of a function.

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

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

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

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

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

At point of inflection,

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

The point where the second derivative of a function is zero

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

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

At maximum point,

____ is also known as the composite function rule

The L'Hospital rule was formulated by

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

Which of the following is not determinate form?

Which of the following is determinate?

The derivative of csc θ is

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

The quantity 2/(e^x - e^x) is equal to

What is 1 - tanh² x equal to?

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

The integral of sin^m θ cos^m θ dθ can easily be determined by using Wallis formula provided the limits are from

The integral of any quotient whose numerator is the difference of the denominator is the ____ of the denominator

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

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

The value of x in trigonometric substitution with an integrand involving (a² - x²) is

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

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

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

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

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

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

A solid of revolution of a parabola is known as

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

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 + a₁x + a₂x + a₃x + ...

Who invented the symbol "∞" for infinity?

Calculus was invented by

Varignon's theorem is used to determine ____

The other term of derivative is _____

If the first derivative of the equation of a curve is a constant, the curve is ____

Refers to a quantity which does not change its value in a general relationship between variables

An infinite change in an independent variable or in a dependent variable due to a small change in independent variable

At the minimum point of y=f(x)

The biggest rectangle inscribed in a circle is

A method used for finding a root of an equation by successive approximations in the form of the iterations

The operation of finding the derivative of function

A function f is said to have a _____ value at c if there exist an open interval containing c on which f is defined such that f(c) ≥ f(x) for all x in this interval

If the derivative of a function is a constant, then the function is _____

An equation which defines one variable purely in terms of another

In mathematics, a quantity larger than any that can be specified

The integral of a function between certain limits divided by the difference in the abscissas between those limits gives the _____ of the function