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.
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.
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.
1
0
Infinity.
When the limit of x approaches 0 x approaches the value of x approaches 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
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
Because infinity is not a umber, it is usually not treated as a number when computing functions. Instead, you can look for a limit of a function as it approaches infinity. For example, the limit as x approaches infinity of 1/x is 0. Because sine oscillates, it's value constantly moves up and down, and it's value as it approaches infinity is not defined because it does not converge on any one number, as some other functions (like 1/x) do.
Usually, it's here that we're talking about a limit. So, it's not that something divided by infinity (which is not actually a number) is equal to 0, it's that as the limit as n approaches infinity, you'll get zero. So, take lim (n approaches infinity) of 1/n. You could plug some immensely large number in for n (say, 1,000,000,000 - which is getting large but not as big as infinity). If you divide 1 by this number, you're gonna get something so small, you could call it zero. So, it's not that we're dividing by infinity, we're approaching infinity - so plug some huge numbers in and see that you get really really close to zero.