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There are multiple ways to interpret this question-that is, you could mean either (5-x+cosx)/x or 5-x +(cosx/x). The limit of the second option is negative infinity because as x approaches infinity, |cosx/x|≤1, so 5-x+cosx/x is very close to 5-x, and 5-infinity is basically negative infinity. For the first option, we consider that -1≤cosx≤1. This implies that, as x approaches infinity, lim of (5-x-1)/x≤lim of (5-x+cosx)/x≤lim of (5-x+1)/x. Simplifying, we get that, as x approaches infinity, lim of (4-x)/x≤lim of (5-x+cosx)/x≤(6-x)/x. Simplifying our new limits, we get -1≤lim of (5-x+cosx)/x≤1. It is now clear that the limit of (5-x+cosx)/x as x approaches infinity =negative 1.

Q: What is the Limit as X approaches infinity 5-X plus cosXoverX?

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As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)

As the number of iterations approaches infinity, the sum approaches 1.

The "value" of the function at x = 2 is (x+2)/(x-2) so the answer is plus or minus infinity depending on whether x approaches 2 from >2 or <2, respectively.

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.

Undefined: You cannot divide by zero

Related questions

As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)

Infinity.

As the number of iterations approaches infinity, the sum approaches 1.

The "value" of the function at x = 2 is (x+2)/(x-2) so the answer is plus or minus infinity depending on whether x approaches 2 from >2 or <2, respectively.

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.

Undefined: You cannot divide by zero

-5

(x-2) is not a factor of the numerator and so y tends to minus infinity as x approaches 2 from below. As x approaches 2 from above, y tends to plus infinity. There are, therefore, no maximum or minimum values for y.

Infinity plus infinity is without beginning nor ending

2

infinity

Negative infinity plus negative infinity equals negative infinity.