To emphasize once again, in evaluating a limit at x = a, we are not concerned with what value f(x) assumes at precisely x = a; we are concerned with only how f(x) behaves as x approaches or nearly becomes a, whether from the left hand or right …

2023年4月2日 · LHL is the value to which the function approaches when it approaches the point from the left and the RHL is the value to which the function approaches when it approaches the point from the right. Basically, LHL and RHL describe the behavior of the function at the immediate left and immediate right of the input value respectively.

2021年7月17日 · $\begingroup$ The question Continuity of differentiable function $x^2\sin(1/x)$ demonstrates that the LHD,RHD of $f(x)$ are in fact $0$ at $x=0$, but the LHL and RHL of $f'(x)$ at $0$ do not exist (the answer only shows that the limit doesn't exist using certain subsequences, but the general statement sort of follows once you see that $\sin ...

2024年9月10日 · Limits, Continuity, and Differentiability are fundamental concepts in calculus, essential for analyzing and understanding the behavior of functions. These concepts are crucial for solving real-world problems in physics, engineering, and economics.

2025年2月2日 · Limits are a fundamental concept in calculus that allows us to understand how functions behave as their inputs approach certain values. Limits are essential for defining derivatives and the related definite integrals. They help us analyze how functions behave locally around specific points of interest.

2018年3月14日 · I've to find the limit of $\dfrac{\sin([x])}{[x]}$ at $x \to 0$. I got the LHL as $\sin(1)$. According to the book, the RHL is outside domain. So, Limit exists. Could someone please explain how the RHL is out of domain? P.S.: $[.]$ is Greatest Integer Function.

2022年9月18日 · (1) The limit exists IF AND ONLY IF both LHL and RHL exist (and are finite). There are no additional criteria for the existence of a limit. (2) The function is continuous if the limit as $x\to a$ is equal to $f(a)$. Here, the function is discontinuous (which is a removable discontinuity), but the limit very much exists. $\endgroup$

Standard limits formulas will help students to do a quick revision before the exam. A limit is a value that a function approaches as the input approaches some value. In this article, we will find the standard limits formulas and some solved examples. …

To decide if a function f(x) is defined at an input value x = a, the following are examined. It is important to note that the L'Hospital's rule is applicable only if the limit exists. The discussion in this topic is about finding if the limit exists or not. So the L'Hospital's rule is not used in finding the limits. Function is continuous.

Therefore, RHL exists and LHL does not exist for the given limit. Hence, option (b) is the correct answer. Note: One can directly put x = 8 to the given relation and get \[\dfrac{\sin \left\{ -2 \right\}}{\left\{ 2 \right\}}\] where {- 2} and {2} will be zero.