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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

Solve this without using log and please show steps. Left parenthesis 4 over 7 right parenthesis superscript x equals 49 over 16?

49/16 = (7^2)/(4^2) = (7/4)^2 = ((4/7)^-1)^2 = (4/7)^-2

Thus as (4/7)^2 = 49/16 and 49/16 = (4/7)^-2

(4/7)^x = (4/7)^-2

Therefore x = -2.

Solve this equation 0.5x- -x plus 3 x-5?

There appears to be no equation in the question: only some disjoint expressions. Expressions cannot be solved.

How could one invent a simple non latinised Vietnamese writing totally different from existing ones?

You can invent a number of symbols, one for each sound. However, inventing a writing that uses existing characters (for example, Latin) would be more practical, since support for such a script is widely available (for example, to type text on a computer).

What is 20 y in a s?

20 y in a s means 20 years in a score

Ex. 4 scores and 7 years=87 years

How can you get into calculus?

Typically, the pre-requisite for calculus is algebra and trigonometry. These are usually universally required because you need these skills to actually do the mathematics of the calculus. There are a lot of identities in trigonometry that you will wish you could remember when you are working with calculus of trigonometric functions.

How is a complex number used?

A complex number, equations and graphs can show electromagnetic forces-for instance two wires carrying current. A formula like (z-1)/(z+1) can show the fields around two parallel wires.

Why does a plus b times a minus b work what is special about it and why does it work in questions like the root 6 plus root 5 times root 6 minus root 5 what is special about the answer?

(a + b)*(a - b) = a2 - ab + ab - b2 = a2 - b2

The expression is often referred to as DOTS = Difference Of Two Squares. What is special about it is that the answer contains only the squares of the two terms while the cross-products cancel out.

So (√6 + √5)*(√6 - √5) = (√6)2 - (√5)2 = 6 - 5 = 1

The above result is used to simplify surds and, in particular, to rationalise their denominators.

What is -8.3 equals x plus 6.1?

x + 6.1 = -8.3

Subtract 6.1 from each side:

x = -14.4

What is y equals 2xexponent2 plus 3x-1?

y=2x2 + 3x-1

To find the zeros of this equation (when y=0) set the equation = 0

0=2x2 + 3x-1

Now, you can either graph the equation in a graphing calculator and find the x intercepts (where the function crosses the x-axis and y=0) or you can factor the quadratic equation by "smiling" or reverse foiling. However, this equation cannot be easily factored. Therefore, using a graphing calculator will provide the correct answer of x= -1.780776 and x= 0.28077641

You can also use the quadratic formula

where the general form of a quadratic equation is ax2 +bx+ c=0=y

In order to use the quadratic formula, you simple plug the corresponding values into the x= equation. This will produce the same results as graphing and finding the x intercepts.

When y equals 2 when x equals 3?

y = x - 1

Or an infinite number of other equations. You'll need to be more specific.

How do you solve the equation x2 - 5x plus 5 equals 0?

Use the quadratic formula:

x = [-b +&- SQRT (b2-4ac)]/2a

where a,b,c are coefficients of the quadratic equation in the form of ax2+bx+c. So in your example a=1, b=-5, c=5

x = [-(-5) + SQRT(52-4*1*5)]/2*1 & x = [-(-5) - SQRT(52-4*1*5)]/2*1

x = [5 + SQRT (5)] / 2 & x = [5 - SQRT(5)]/2

How do you easily balance and solve a scientific equation?

A scientific equation is basically a math equation. Those come in different kinds; each kind needs special techniques for solving. In the simplest case, you have to solve for a single variable; try to transform the equation so that your variable is on the left, and anything else is on the right.