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ozkan12
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if $\lim_{{n}\to{\infty}} {y}_{m+1}={x}^{*}$, Can we say that $\lim_{{n}\to{\infty}} {y}_{n-1}={x}^{*}$...Please pay attention, I say m and n...
ozkan12 said:if $\lim_{{n}\to{\infty}} {y}_{m+1}={x}^{*}$, Can we say that $\lim_{{n}\to{\infty}} {y}_{n-1}={x}^{*}$...Please pay attention, I say m and n...
If
$$\lim_{m\to\infty}y_{m+1}=x^*,$$
can we say that
$$\lim_{n\to\infty}y_{n-1}=x^*?$$
A limit is the value that a function or sequence approaches as its input or index approaches a certain value. In this case, we are looking at the limit of a function as the inputs approach infinity.
To determine the limit of a function, we can use various methods such as algebraic manipulation, graphing, or using limit laws. In the case of x* when n and m approach infinity, we can use the limit laws to simplify the expression and determine the limit.
Using infinity in limits allows us to evaluate the behavior of a function as its inputs approach an infinitely large value. This can help us understand the overall trend or behavior of a function as it approaches infinity.
Yes, a function can have a limit when n and m approach infinity. This is known as an infinite limit and it means that the function's output is approaching an infinitely large value as its inputs approach infinity.
Limits are a fundamental concept in calculus and are used to define derivatives and integrals. They help us understand the behavior of a function as it approaches a certain value, which is crucial in solving problems in calculus such as finding the slope of a curve or the area under a curve.