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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
cos x equals cos -x because cos is an even function. An even function f is such that f(x) = f(-x).
How do you get 6 ltr from a 7 ltr jar and a 4 ltr jar?
Fill 4 ltr jar State of two jars: (4, 0)Pour from 4 ltr to 7 ltr: (0, 4)
Refill 4 ltr: (4, 4)
Pour from 4 ltr to 7 ltr jar until it is full: (1, 7)
Empty 7 ltr: (1, 0)
Pour from 4 lts to 7 ltr: (0, 1)
Fill 4 ltr: (4, 1)
Pour from 4 ltr to 7 ltr jar: (0, 5)
Fill 4 ltr: (4, 5)
Pour from 4 ltr to 7 ltr jar until it is full: (2, 7)
Empty 7 ltr: (2, 0)
Pour from 4 lts to 7 ltr: (0, 2)
Fill 4 ltr: (4, 2)
Pour from 4 ltr to 7 ltr jar: (0, 6)
Done.
Which ordered pair will be included on the graph for y equals plus 9 plus x?
All those where y is 9 more than x will be included on the graph of y = 9 + x.
eg (0, 9), (1, 10), (-5, 4).
What will happen When the amplitude of a body undergoing simple harmonic motion is doubled?
it'll get louder
Is there a particular reason that you cannot use your calcuator?
484*18 = 8712
Can you explain what the function of logarithms are?
The logarithm of a number is another number which, if used as the exponent of a third number, yields the first number.
The third number is called the base. Usually, it is 10 (common logarithm) or e (2.71828..., natural logarithm).
As an example, the common logarithm of 100 is 2. This meets the equation...
102 = 100
... whereas the natural logarithm of 100 is about 4.61...
2.718284.61 = (about) 100
One useful function of logarithms is in the multiplication of numbers. If you want to multiply two numbers, you can either just multiply them, or you can add their logarithms together and do the inverse logarithm (power) of the result. For instance...
10 * 100 = 1000
log10 10 = 1
log10 100 = 2
1 + 2 = 3
103 = 1000
This technique is used in slide rules, and it can also be used visually, to come up with a rough estimate of the product of two numbers.
well, you have to combine the like terms so put the X's together 3X + 2X = 5X and then add the left over numbers together so; 3 + 10 = 13. So you have made the sum easier now it is 5X + 13. You haven't displayed the answer to this question so i cannot work out the rest for you, but what you have to do for example say the answer was: 133, you do 133 - 13 = 120 then divide 120 by 5 = 24 so the example answer would be 24.
How do you calculate critical points of derivatives?
The "critical points" of a function are the points at which the derivative equals zero or the derivative is undefined. To find the critical points, you first find the derivative of the function. You then set that derivative equal to zero. Any values at which the derivative equals zero are "critical points". You then determine if the derivative is ever undefined at a point (for example, because the denominator of a fraction is equal to zero at that point). Any such points are also called "critical points".
In essence, the critical points are the relative minima or maxima of a function (where the graph of the function reverses direction) and can be easily determined by visually examining the graph.
How do you solve logx minus 3 plus log 4 equals log x?
Use the identity log(ab) = log a + log b to combine the logarithms on the left side into a single term. Then take antilogarithms (just take the log away) on both sides.
What is the limit of x divided by e to the x as x approaches negativ infinity?
lim x -> -inf [x/ex] = lim x -> +inf[-x/e-x] = - lim x -> +inf [ xex ] = -inf
If you want to see this function then I suggest you use either:
(a) wolframalpha.com: put in show me x/exp(x)
or (b) geogebra, which is available for the desktop.
What are the intercepts of -4x - 5z equals 60?
(0, -12) and (-15, 0)
(0, -12) and (-15, 0)
(0, -12) and (-15, 0)
Why does a negative number multiplied by a negative number equals a positive number?
This is NOT a proof, just an explanation.
Imagine you are on a number line and you are walking. Multiplying x*y is taking x steps, each of size y. Negative steps are interpreted by requriring you to face the negative end of the line before you start walking and negative step sizes are backward where backward is heel first. This mean to find, -x*-y you stand on zero, face in the negative direction, and then take x backward steps, each of size y.
Formula for solving X2 plus -2x -5.25 equals 0?
x2-2x-5.25 = 0
When factored:
(x-7/2)(x+3/2) = 0
Therefore: x = 7/2 and also x = -3/2
To solve a quadratic equation use the formula:
x = -b/2a + and also - the square root of b2-4ac over 2a
Whereas in this particular equation: a = 1, b = -2 and c = -5.25
