I don't get the same answer for that limit. Please post your detailed working.ilhamGD said:It means that a=1, and after using the formula for A^n-B^n the limit when x< 2 becomes -(2^n-1+2^n-2+...+1) which is -2^(n-2) and then I can find b which is -2^(n-1)/3
can u tell me if that is correct ? and should I also find f(2)?
A function is considered continuous at a specific point if the function exists at that point, the limit of the function at that point exists, and the limit and the function value at that point are equal.
We can determine the value of a and b by setting up an equation that satisfies the conditions for continuity at 2. This includes ensuring that the function exists at 2, the limit of the function at 2 exists, and the limit and the function value at 2 are equal. We can then solve for a and b using algebraic methods.
A function being continuous at a point means that there are no breaks or jumps in the graph at that point. This is important because it allows us to make accurate predictions and calculations using the function, as well as make connections between different parts of the function.
Yes, there are specific methods such as using the definition of continuity, using the intermediate value theorem, or using the properties of continuity to solve for a and b. It ultimately depends on the specific function and the given conditions.
No, a function cannot be continuous at a point if it is not defined at that point. In order for a function to be continuous at a point, it must exist at that point.