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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
Why can you not divide a number by 0?
You can't divide something like 5 by nothing. It's irrational, because the number zero represents nothing, and that it is just a symbol recognizing that nothing is there. It's almost like an invisible thing, because 0 represents invisibility, because it is the only symbol justifying nothing in the numerical system.
What is eighty-two percent written as a fraction in simplest form?
Expressed as a proper fraction in its simplest form, 82 percent is equal to 41/50 or forty-one fiftieths.
Asymptote of x² times e to the power of x?
As x tends to negative infinity, the expression is asymptotically 0.
What capacity are 1997 Chevy Cheyenne gas tanks?
The capacity of a 1997 Chevy Cheyenne gas tank is 128 liters. Or one could say it is 32 gallons.
Weight is measured in Newtons, not kg. A kilogram measure mass.
The density is approx 2.7 grams/cubic cm.
How do you round 87 and frame the first digit?
you should round it to the nearest tenth and box the first number
20 = -4f + 6 + 14
Subtract 20 from each side:
0 = -4f
Divide each side by 4:
f = 0
How do you factor 12x2 plus 28x-17?
The trick with this kind of question is to find two terms that add up to the middle one (28x), and whose coefficients are equal multiples of the first and last term:
12x2 + 28x - 17
= 12x2 - 6x + 34x - 17
= 6x(2x - 1) + 17(2x - 1)
= (6x + 17)(2x - 1)
The only trick with this technique is that sometimes it's difficult to find those two middle terms (-6x and 34x in this case). If it takes too long to figure this out, you can actually break it down into ~another~ quadratic equation, which will usually be easier to factor, and give you those two values. Consider:
Let "a" and "b" be the unknown coefficients. We know:
b = 28 - a <-- we know this because they must add up to the middle term
12/a = b/17 <-- this must be true in order for us to end up with a common multiple.
∴ 12/a = (28 - a)/17
∴ 28a - a2 = 204
∴ a2 - 28a + 204 = 0
We can then solve for "a" by factoring this equation:
(a - 34)(a + 6) = 0
So our coefficients are the two possible values for "a", 34 and -6. We can then simply plug them in to the original equation and factor it out as shown above.
What is the answer to 5x plus 6 equals 1divided by 4 times 13x-11?
5x + 6 = 1 / 4(13x-11)
(5x+6)(4)(13x-11)= 1
4(65x2-55x+78x-66)=1
260x2 +92x-264-1=0
260x2+92x-263=0
Graph y = 260x2 +92x -263 and find its zero or use the quadratic formula
Six x squared plus twenty one x - forty five?
Assume the question refers to solving the quadratic equation 6x2 +21x - 45 = 0, then :-
This equation can be factored 6x2 + 21x - 45 = (6x - 9)(x + 5) = 0
This holds true when either 6x - 9 or x + 5 = 0
When 6x - 9 = 0 then x = 9/6 = 1.5 : When x + 5 = 0 then x = -5
Find the relative maximum of -x2 plus 6x-4?
f(x) = -x2 + 6x - 4
∴ f'(x) = -2x + 6
Solve for f'(x) = 0:
0 = -2x + 6
x = 3
So the peak occurs at the point where x = 3. Now you can calculate the value of f(3)
f(3) = -32 + 6(3) - 4
∴ f(3) = -9 + 18 - 4
∴ f(3) = 5
So the maximum value of that function is 5, and it occurs when x = 3.
To prove that it's a maximum, take the second derivative:
f'(x) = -2x + 6
∴ f''(x) = -2
Because it's negative, we know that this is the peak of the curve.
How do you foil 1 plus 2sinx plus sin2 x?
sin2(x) + 2 sin(x) + 1
It might be easier for you if you use 'S' temporarily to represent 'sin(x)', just long enough to look at it.
Then you have
S2 + 2S + 1
Can you 'foil' that ?
It's just the square of (S + 1). The factors are (S+1) and (S+1).
The original expression is the square of [sin(x) + 1].
2x^2+2x-14
(-2 +- sqrt(2^2 -4(2)(-14))/2(2)
simplifies to
+- sqrt 29
So your answers would be, sqrt(29), and, -sqrt(29)
