Calculus Elements (MESL)

The differential equation y” - 5x(y’)⁴ = eˣ + 1 is of order

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

The numbers which are represented with letters.

When an equation involves one or more derivatives with respect to a particular variable, then that variable is called:

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

A solid of revolution of a parabola is known as

The integrating factor of the differential equation ydx - xdy = 0 is

The differential equation d²y/dx² + 5 dy/ dx + 6y² = 0 is

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

Varignon’s theorem is used to determine ___.

The n arbitrary constants will be eliminated from the ___ equation to obtain a differential equation of order n.

Which of the following best described a linear differential equation?

The derivative of csc θ is

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

The derivative of a function is identical to the ___ of the graph of the function.

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

An equation in which all terms are of the same degree

At the point of inflection where x = a,

The ___ of a relation is the set of first elements of pairs in the relation.

In the function y = f(x), x is termed

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

If the unknown function depends on two or more independent variables, the differential equation is:

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

Calculus was invented by

which of the following is not determinate form?

If the 2nd derivative of the eq. of a curve is equal to the negative of the eq. of that same curve, the curve is

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

The ___ of a relation is the set of second elements of the pair in the relation.

The ___ of the function is the rate of change of the slope of the graph.

What is the point where the second derivative is zero?

What is 1 - tanh² x equal to?

The differential equation (y’”) 3 - 5x(y’)⁴ = eˣ + 1 is of degree

The absolute value of a nonzero number is:

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

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

The integral of sinᵐ θ cosⁿ θ dθ can easily be determined by using Wallis formula provided limits are from

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

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

The coefficients of dx and dy of the equation x²ydx + (x³ + y³)dy = 0 are homogeneous functions of degree

At maximum point,

At the point of inflection,

The derivative of aᵘ with respect to x is

If the unknown function depends only on one independent variable, the differential equation is:

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

A ___ section of a surface of revolution is the section containing the axis of revolution

It is a differential equation in the form y’ + P(x)y = Q(x)yⁿ

Equations whose members are equal only for certain or possibly no value of the unknown.

The L’Hospital rule was formulated by

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

The differential equation of all straight lines whose slope is m and whose y-intercept is b.

Which of the following equation below is a solution of y’ + y = 5

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

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

Any set of ordered pair is called a

If the degree of the numerator is one more than the degree of the denominator, the quotient is a ___ polynomial.

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

Who invented the symbol “∞” for infinity?

Equations whose members are equal only for certain or possibly no value of the unknown.

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

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

What is described?

Which of the following is determinate?

The general solution of an ordinary differential equation of order n contains ___ arbitrary constants.

Any function of y/x is homogeneous of degree:

if y = tanhx, find dy/dx

What is the process called?

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

Any multiplier which transforms a differential equation into an exact differential equation is called a/an:

What is described?

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

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

If dQ/dt = kQ then Q is equal to:

All numbers multiplied by ___ equals unity.

from the picture, what is the answer?

The operation of finding the derivative of a function.

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

The degree of a polynomial or equation is the

What is described?

The differential equation of the form y’ = f(x)y + h(x)y² is called as:

Evaluate the Integral of tanh u du

___ is also known as the composite function rule.

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

A function F(x) is called ___ of f(x) if F’(x) is f(x).

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

A function f(x,y) is called a homogeneous function of the nth degree if :

what is described?