Diffential calculus.docx

DifferentialCalcQuestText Choice1 Choice2 Choice3 Choice4 Subj

__________is also known as the composite function rule. Chain rule Trapezoidal rule Simpson’s rule

L’Hospital’s rule

Differential Calculus

A function F(x) is called _________ of f(x) if F’(x) = f(x). Antiderivative Derivative Implicit function

Explicit function


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

Point of inflection Point of deflection

Point of intersection

Yield point Differential Calculus

A point on the curve where the second derivative of a function is equal to zero is called Inflection point Minima Maxima Critical point Differential Calculus

A printed page must contain 60 sq. m. of printed material. There are to be margins of 5 cm. on either side and margins of 3 cm. on top and bottom. How long should the printed lines be in order to minimize the amount of papers used?

10 18 12 15 Differential Calculus

A statue 3 m. high is standing on a base of 4 m. high. If an observer’s eye is 1.5 m. above the ground, how far should he stand from the base in order that the angel subtended by the statue is maximum?

3.71 3.71 4.41 3.51 Differential Calculus

A window composed of a rectangle surmounted by an equilateral triangle has a total perimeter of 15 m. Find its width if it admits the maximum amount of light.


An isosceles triangle with equal sides of 20 cm. has these at variable equal angles with the base. Determine the maximum area of the triangle.


At a point where y’ = 0, if y changes from positive to negative as x increases, Y is maximum X is minimum Y is minimum X is maximum Differential Calculus

At point of inflection, Y” = 0 Y’ = 0 Y” is negative Y” is positive Differential Calculus

At the minimum point, the slope of the tangent line is Zero Infinity Positive Negative Differential Calculus

Evaluate the limit (x - 4)/( x^2 - x -12) as x approaches 4. 1/7 Undefined 0 Infinity Differential Calculus

Evaluate the limit of (x - 4) / (x^2 - x - 12) as x approaches 4. 1/7 0 undefined infinity Differential Calculus

Find dy/dx of y = 3 sin 2x. 6 cos 2x 6 cos x 3 cos 4x 3 sin 2x Differential


CalculusFind the equation of the axis of symmetry of the function y = 2x^2 - 7x + 5. 4x - 7 = 0 7x - 4 = 0 x - 4 = 0 x - 7 = 0 Differential

CalculusFind the point in the parabola y^2 = 4x at which the rate of change of the ordinate and abscissa are equal.

(1,2) (2,1) (4,4) (-1,4) Differential Calculus

Find the point of inflection of f(x) = x^3 – 3x^2 – x + 7 1, 4 1, 2 2, 1 3, 1 Differential Calculus

Find the radius of a right circular cone having a lateral area of 544.12 sq. m. to have a maximum volume.


Find the radius of curvature of the curve y = 2x^3 + 3x^2 at (1, 5). 97 90 101 87 Differential Calculus

Find the second derivative of y = x -2 when x = 2. 0.375 0.268 0.148 0.425 Differential Calculus

Find two numbers whose sum is 20, if the product of one by the cube of the other is to be a maximum.

5 and 15 10 and 10 4 and 16 8 and 12 Differential Calculus

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 sinusoid A paraboloid A cissoid An exponential


If y = tanhx, find dy/dx Sech2 x -sech2 x Sech x tanh x -sech x tanh x Differential Calculus

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

Minimum points Maximum points

Stationary points


The critical points of a graph occur where the derivative of a function is Zero or approaches infinity

Approaches infinity

Zero Either 1 or -1 Differential Calculus

The derivative of a function is identical to the________ of the graph of the function. Slope Secant Tangent Normal Differential Calculus

The derivative of au with respect to x is Au ln a Au ln u Ua ln a Ua ln u Differential Calculus

The diameter of a circle is to be measured and its area computed. If the diameter can be 64 16 32 48 Differential


measured with a maximum error of 0.001 cm. and the area must be accurate to within 0.10 sq.cm. find the largest diameter for which the process can be used.

Calculus

The function y = (x-4)/(x+2) is discontinuous at x = ? -2 0 1 2 Differential Calculus

The L’Hopitals rule was formulated by J. Bernoulli Marrione de L’Hopital

Marquis de L’Hopital

I. Newton Differential Calculus

The operation of finding the derivative of a function. Differentiation Differentiating Differential Integrating Differential Calculus

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

Minima Maxima Point of inflection

Critical point Differential Calculus

The point where the first derivative of a function is zero and the second derivative is positive. Minimum point Maximum point Point of inflection

Critical point Differential Calculus

The point where the second derivative of a function is zero. Point of inflection Minimum point Point of intersection

Maximum point


The sides of a triangle are 8, 15 and 17 units. If each side is doubled , how many square units will the area of the new triangle be?


The volume of the sphere is increasing at the rate of 6 cm^3/hr. At what rate is its surface area increasing (in cm^2/hr) when the radius is 50 cm?


The_________ derivative of a function is the rate of change of the slope of the graph. Second First Third Fourth Differential Calculus

Water running out a conical funnel at the rate of one cubic inch per second. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 inches from the top.

-1/9pi in/sec -4/9pi in/sec 2/3pi in/sec -3/2pi in/sec Differential Calculus

What is the limit of cos(1/y) as y approaches infinity? 1 0 -1 infinity Differential Calculus

What is the point where the second derivative is zero? Inflection point Minima Maxima Point of intersection


When f”(x) is negative the curve of y = f(x) is concave_____________. Downward To the right Upward To the left Differential Calculus


Who invented the symbol for infinity? John Wallis John Venn John Stockton John Napier Differential Calculus

DifferentialEqn

QuestText Choice1 Choice2 Choice3 Choice4 Subj

Determine the general solution of xdy + ydx = 0.

xy = C ln x + ln y = C x + y = C ln (xy) = C Differential Equation

Solve (cos x cos y - cot x) dx - sin y dy = 0

Sin x cos y = ln (c sin x)

Sin x cos y = ln (c cos x)

Sin x cos y = - ln (c sin x)

Sin x cos y = - ln (c cos x)

Differential Equation

The equation y^2 = cx is the general equation of

y' = y / 2x y' = 2x / y y' = 2y / x y' = x / 2y Differential Equation

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Diffential calculus.docx