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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
Does the graph of x equals -3 represent a vertical graph?
Yes, x = -3 would represent a vertical line at abscissa -3, parallel to the y-axis.
A pendulum moves in simple harmonic motion. If a graph of the pendulum's motion is drawn with respect with respect to time, the graph will be a sine wave. Pure tones are experienced when the eardrum moves in simple harmonic motion. In these cases "wave" refers not to the thing moving, but to the graph representing the movement.
Does heart stop before hit ground when falling?
No. Only if you have a heart condition and time to contemplate your predicament.
CRO consists of a cathode ray tube which is having the vacuum conditions . The electron beam is emitted by a cathode at the rear end of the tube. This beam is accelerated and focused by one or more anodes. The rays then strike the front (other end) of the tube and produces a bright spot on the phosphorescent screen
If 4x-7 equals 2x plus 5 What is x?
4x - 7 = 2x + 5
Add 7 to each side ==> 4x = 2x + 12
Subtract 2x from each side ==> 2x = 12
Divide each side by 2 ==> x = 6
Why do some shapes tessellate and some don't?
Tessellation is repeating a pattern over and over and filling an area with no overlaps and no gaps. Some shapes can't do this, because they don't fit with themselves without leaving big gaps between the parts.
s = 11*t/sqrt(46).
How can you use Status quo in a sentence?
For them the movement is giving voice to a social discontent with the social status quo.
Negative square roots are just the opposite of positive square roots. Since square roots (of positive numbers) are real, the negative square roots are also real.
Square roots of negative numbers are not real.
Note that -1 = exp(Pi*i), so (-1)^(1/2) = exp((1/2)*Pi*i) = i.
Note that exp(i*x) = cos(x) + i*sin(x), for instance by taking derivatives:
(d/dx)(exp(i*x)) = i*exp(i*x), and
(d/dx)^2(exp(i*x)) =(-1)*exp(i*x).
This means that the second derivative of exp(i*x) equals -exp(i*x).
The same property holds for cos(x) + i*sin(x):
(d/dx)(cos(x) + i*sin(x)) = -sin(x) + i*cos(x)
(d/dx)^2(cos(x) + i*sin(x)) = -cos(x) - i*sin(x) = -(cos(x) + i*sin(x)))
Hence cos(x) + i*sin(x)) = C + Dx + exp(i*x), for some C and D.
Comparing the values on both sides for x = 0, we find:
1 = C+1, so C = 0 and for the first derivative:
i = D + i, so D = 0.
So cos(x) + i*sin(x)) = exp(i*x) for all x.
by comparing x=0 for both functions and their first derivative. Since they coincide,
What is the function from f1 to f12?
If you mean the function keys on the keyboard, they don't have a standard definition. The usage of the keys depends on the specific program. F1 is usually standardized as the help key; the other keys depend on the program you are using.
How do you graph trigonometric functions?
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
What is the answer to 2x times x plus 3 equals 100?
2X * X + 3 = 100
do what it says; multiply
2X2 + 3 = 100
subtract 3 from each side
2X2 = 97
divide each side by 2
X2 = 97/2
take square root both sides
X = sqrt(97/2)
you could rationalize the denominator by this method, form of one
X = sqrt(97/2)
same as saying
X = sqrt(97)/sqrt(2) ( use sqrt(2)/sqrt(2) as form of one )
X = sqrt(97)/sqrt(2) * sqrt(2)/sqrt(2)
X = sqrt(194)/2
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You have to enter what you use to log in a computer if ur a student
What shape would the graph of U versus x have if a particle were in a region of neutral equilibrium?
In neutral equilibrium, displacement in either direction would not affect the potential energy of the particle, therefore, the graph would be horizontal.
How do you solve three nonlinear equations in three parameters?
There isn't a universal way to do this, just like there isn't a universal way to solve nonlinear equations in one variable. A good place to start, however, would be to attempt to solve an equation for one of the variables, in terms of the other two. If you substitute that into the other equations, you will then have a system of two equations in two variables. Do this again, and you'll have a single variable equation that you'll hopefully know how to solve.
No. Above x = 2/3, the slope of the x-cubed function is larger than that of the x-squared function. So, for example, a counter-example for the claim is the set of points 0.7 and 0.8.
How might you eliminate the x-term from the top equation?
Clearly, it has already been eliminated since I cannot see any x in the top equation!
Condition for the continuity and differentiablity of a function?
An intuitive answer (NOTE: this is far from precise!)
A function is continuous if you can trace its graph without lifting your pencil from the page. If, additionally, it is smooth everywhere without any jagged edges or abrupt corners, then it is differentiable. It is not possible for a function to be differentiable but not continuous. On the other hand, plenty of functions are continuous without being differentiable.
5x2-16x+12 = (5x-6)(x-2) when factored
There is no rational factorisation to this expression.
