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F(x)=sin 1/x,&x ne0\\ 1,&x=0 (a) removable discontinuity at x = 0 (d) continuity at x = 0 (b) non-removal discontinuity at x = 0 (c) mined discontinuity at x = 0 14. The function?
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F(x)=sin 1/x,&x ne0\\ 1,&x=0 (a) removable discontinuity at x = 0 (d) ...
The function f(x) = sin(1/x) can be defined for all non-zero values of x. However, it is important to note that the behavior of this function near x = 0 is quite different compared to other values of x.
As x approaches 0 from the positive side, the function oscillates infinitely between -1 and 1. This is because as x gets smaller, the value of 1/x becomes larger, causing the sine function to fluctuate rapidly.
On the other hand, as x approaches 0 from the negative side, the function still oscillates between -1 and 1, but with opposite sign. This is because the negative values of 1/x result in a reflection of the graph across the y-axis.
In summary, the function f(x) = sin(1/x) exhibits rapid oscillations near x = 0, taking on all values between -1 and 1 infinitely many times. However, for non-zero values of x, the function behaves similarly to a regular sine function.
As x approaches 0 from the positive side, the function oscillates infinitely between -1 and 1. This is because as x gets smaller, the value of 1/x becomes larger, causing the sine function to fluctuate rapidly.
On the other hand, as x approaches 0 from the negative side, the function still oscillates between -1 and 1, but with opposite sign. This is because the negative values of 1/x result in a reflection of the graph across the y-axis.
In summary, the function f(x) = sin(1/x) exhibits rapid oscillations near x = 0, taking on all values between -1 and 1 infinitely many times. However, for non-zero values of x, the function behaves similarly to a regular sine function.
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F(x)=sin 1/x,&x ne0\\ 1,&x=0 (a) removable discontinuity at x = 0 (d) continuity at x = 0 (b) non-removal discontinuity at x = 0 (c) mined discontinuity at x = 0 14. The function?
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