Can you explain, what ##sen## means and where the ##1## in your antiderivative comes from?Genilson said:
I believe it is another abbreviation for sine.fresh_42 said:
Are you allowed to use ##\lim_{x \rightarrow 0}\frac{\sin (x)}{x}=1##? If so, you could cancel the quotient by an ##x##.Genilson said:
And a ##2## in the nominator, which tells you?Genilson said:
You'd probably ignored the absolute value of your denominator. How do you manage to get a negative number?Genilson said:
##\sin x## and ##x## are pretty much the same in a small neighborhood around zero, aren't they? This means ##\frac{\sin x}{x} \, \approx \,1##.Genilson said:
A limit with integral and absolute value is a mathematical concept used to determine the behavior of a function as the input approaches a specific value. It involves taking the absolute value of the difference between the function's output and a given limit value, and then integrating this absolute value function to find the area under the curve.
A limit with integral and absolute value allows us to analyze functions that may not have a defined value at a certain point, such as when the function approaches infinity. It can also help us determine the convergence or divergence of certain series, and can be used to find the area between curves.
To calculate a limit with integral and absolute value, we first take the absolute value of the difference between the function's output and the given limit value. We then integrate this absolute value function over the interval between the limit value and the input value. The result of this integration will give us the area under the curve, which can then be used to determine the limit's behavior.
A limit with integral and absolute value is commonly used in calculus to solve problems related to finding the area under a curve, as well as determining the convergence or divergence of series. It is also used in physics and engineering to analyze the behavior of physical phenomena, such as electric fields and fluid flow.
One limitation of using a limit with integral and absolute value is that it can be difficult to compute for more complex functions. It also may not always provide an accurate representation of the function's behavior, as it is only an approximation. Additionally, it may not work for certain types of functions, such as those with discontinuities or infinite oscillations.