Here, just plug x=0 into x^2 to get 0^2=0. The limit is 0.
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Actually 0/0 is undefined because there is no logical way to define it. In ordinary mathematics, you cannot divide by zero.The limit of x/x as x approaches 0 exists and equals 1 so you might be tempted to define 0/0 to be 1.However, the limit of x2/x as x approaches 0 is 0, and the limit of x/x2 as x approaches 0 does not exist .r/0 where r is not 0 is also undefined. It is certainly misleading, if not incorrect to say that r/0 = infinity.If r > 0 then the limit of r/x as x approaches 0 from the right is plus infinity which means the expression increases without bounds. However, the limit as x approaches 0 from the left is minus infinity.
The limit of cos2(x)/x as x approaches 0 does not exist. As x approaches 0 from the left, the limit is negative infinity. As x approaches 0 from the right, the limit is positive infinity. These two values would have to be equal for a limit to exist.
The limit is 0.
When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right. For example, let's look at the function 1/x as x approaches 0. As it approaches 0 from the left, it travels towards negative infinity. As it approaches 0 from the right, it travels towards positive infinity. Therefore, the limit of the function as it approaches 0 does not exist.
In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)