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huan.conchito
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[itex]
Lim x->2^+ [Sqrt (x-2)] (1/x-1/2) [/itex]
Please help I am having trouble taking this limit
Lim x->2^+ [Sqrt (x-2)] (1/x-1/2) [/itex]
Please help I am having trouble taking this limit
huan.conchito said:yes, when i plug in [itex]2^+[/itex] i can't get a real number
The limit as x approaches 2 from the right is the value that a function or sequence approaches as the input (x) gets closer and closer to 2 from values greater than 2. It is denoted as lim x→2⁺ f(x).
To determine the limit as x approaches 2 from the right, you can either plug in values close to 2 from the right side into the function and observe the resulting output, or use algebraic techniques such as factoring, simplifying, or finding common denominators to evaluate the limit.
The limit as x approaches 2 from the right is important because it helps us understand the behavior of a function or sequence as the input approaches a specific value. It can also be used to determine if a function is continuous at a given point.
Yes, the limit as x approaches 2 from the right can exist even if the function is not defined at x=2. This is because the limit is concerned with the behavior of the function as x gets closer and closer to 2 from the right, not necessarily the value of the function at x=2.
One common misconception is that the limit must be equal to the value of the function at x=2. This is not always the case, as the limit can approach a different value than the actual function value at that point. Another misconception is that the limit does not exist if the function has a "hole" or removable discontinuity at x=2. The limit can still exist in this case as long as the function approaches the same value from both sides of x=2.