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What are derivatives and why do derivatives exist?
The derivative of a function is another function that represents the slope of the function at each of the points in the original function's domain. For instance, given the function f(x) = x2, the derivative is f'(x) = 2x. This says that the slope of the original function f(x) = x2 is 2x at every x. This is very useful when you want to graph the function, because you only need a few data points, and then you can quickly sketch the shape of the curve when you know the slope. Later on, you are going to learn about anti-derivatives, and you are going to call them integrals, and you are going to learn the vast power of this thing we call calculus in terms of finding the area under a curve, but let's take it one step at a time.
Could Give and explain the two basic classifications of calculus?
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.
The area under the normal curve is greatest in which scenario?
The area under the normal curve is ALWAYS 1.
What does the area under the curve equal?
The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
What is the difference between differentiation and integration?
Differentiation involves determination of the slope, i.e. the derivative, of a function. The slope of a function at a point is a straight line that is tangent to that function at that point, and is the line defined by the limit of two points on the original curve, one of those two points being the point in question, as their distance between each other becomes zero. There are several things you can do with derivatives, not the least of which is aid in plotting functions and finding various minima and maxima. Integration involves determination of the inverse-slope, i.e. the integral, of a function. The integral of a function is another function whose derivative is the first function. There are several things you can do with integrals, not the least of which is finding the area or volume under or in a curve or shape.
Relationship between integral and derivative?
The Derivative is the instantaneous rate of change of a function. An integral is the area under some curve between the intervals of a to b. An integral is like the reverse of the derivative, Derivatives bring functions down a power, integrals bring them up, in-fact indefinite integrals (ones that do not have specifications of the area between a to b) are called anti derivatives.
What comes to mind when you hear the word calculus?
The first thing that come up into my mind is numbers, calculation, integrals and derivatives
What are real world applications of integrals?
Most likely, you will not be doing integrals as part of your daily life, but knowing how integrals work, can help you understand how some things work. Foir example, the interest earned on an interest bearing account (like a savings account) when compounded daily, is close to the value for 'continuous compounding'. The rate curve represents the interest earned at a particular time, and the area under the curve (the integral of the function) represents the total accumulated interest.
How can you break the area under curve you are finding into smaller pieces so that you can find the true value?
You will need to break the curve into segments each of which can be integrated. Calculate the finite integrals and add them together.If you were thinking of the trapezium method, think again! That does not give the true value - only an approximation.You will need to break the curve into segments each of which can be integrated. Calculate the finite integrals and add them together.If you were thinking of the trapezium method, think again! That does not give the true value - only an approximation.You will need to break the curve into segments each of which can be integrated. Calculate the finite integrals and add them together.If you were thinking of the trapezium method, think again! That does not give the true value - only an approximation.You will need to break the curve into segments each of which can be integrated. Calculate the finite integrals and add them together.If you were thinking of the trapezium method, think again! That does not give the true value - only an approximation.
What are derivatives and why do derivatives exist?
The derivative of a function is another function that represents the slope of the function at each of the points in the original function's domain. For instance, given the function f(x) = x2, the derivative is f'(x) = 2x. This says that the slope of the original function f(x) = x2 is 2x at every x. This is very useful when you want to graph the function, because you only need a few data points, and then you can quickly sketch the shape of the curve when you know the slope. Later on, you are going to learn about anti-derivatives, and you are going to call them integrals, and you are going to learn the vast power of this thing we call calculus in terms of finding the area under a curve, but let's take it one step at a time.
What are some real life applications of indefinite integrals?
One of the major applications of indefinite integrals is to calculate definite integrals. If you can't find the indefinite integral (or "antiderivative") of a function, some sort of numerical method has to be used to calculate the definite integral. This might be seen as clumsy and inelegant, but it is often the only way to solve such a problem.Definite integrals, in turn, are used to calculate areas, volumes, work, and many other physical quantities that can be expressed as the area under a curve.
What is called area under normal curve?
It is called ONE = 1.
Why did limit invented?
Limits were developed in mathematics to describe the behavior of functions as they approach specific values or points. They allow us to analyze and understand the behavior of functions at points where they may not be defined or may have discontinuities. Limits are fundamental in calculus for defining concepts like derivatives and integrals.
Could Give and explain the two basic classifications of calculus?
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.
He area under the standard normal curve is?
The area under the standard normal curve is 1.
What I helps you to find the area under the curve?
If this is on mymaths.co.uk then the answer to this question is: Integration. That is how to find the area under the curve.
The area under the normal curve is greatest in which scenario?
The area under the normal curve is ALWAYS 1.
