Announcement Unfortunately, after over 12 years of providing a free function limits calculator, I had to “turn it off”. The calculator was a simple “widget”
As we all know (for example from my Limits Course), a function is continuous at the point x0 when the left-side limit of this function at this point is equal to the right-side limit of the function at this point and is equal to the value of the function at this point.
If any of the equality is not satisfied, the function f(x) is not continuous at the point x0, and the point is called a point of discontinuity. In this naming, you can go a step further and DISTINGUISH the points of discontinuity. See how to do it.
We have a limit of the function as x approaches infinity from the function f(x)=sinx.
We intuitively feel that the above limit does not exist. x’s are getting bigger and bigger, and the sine values are constantly fluctuating between -1 and 1. But how can we formally demonstrate and prove this?
We usually treat the limits of a sine function as: x tends to zero then{sinx} /x=1.
Question: what about cosine of x? Does it have any “typical” border?
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