lim x -> -inf [x/ex] = lim x -> +inf[-x/e-x] = - lim x -> +inf [ xex ] = -inf
If you want to see this function then I suggest you use either:
(a) wolframalpha.com: put in show me x/exp(x)
or (b) geogebra, which is available for the desktop.
The limit does not exist.
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.
1
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.
0
What is the limit as x approaches infinity of the square root of x? Ans: As x approaches infinity, root x approaches infinity - because rootx increases as x does.
When any number is divided by infinity, the result approaches zero but never actually reaches it. This is because infinity is not a specific number but rather a concept representing unboundedness. Mathematically, the limit of any finite number divided by infinity as infinity approaches infinity is zero.
The limit does not exist.
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.
1
When we divide 1 by infinity, we are essentially taking the limit of 1 as the denominator approaches infinity. In mathematics, this limit is equal to zero. This is because as the denominator becomes infinitely large, the value of the fraction approaches zero. Therefore, 1 divided by infinity equals 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.
0
Infinity.
Limit as x tends to ∞: x/e^xAs you can see, as x approaches infinity, the sum becomes ∞/∞. Now we use l'Hospitals rules.d/dx(x) = 1 (Derivative)d/dx(e^x) = e^x (Derivative)therefore, the sum can be written as lim x tends to ∞ 1/e^xNow as x approaches infinity, the sum = 1/∞ = 0Therefore, lim x tends to infinity: x/e^x = 0
When the limit of x approaches 0 x approaches the value of x approaches infinity.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)