The answer will depend on any parentheses present in the expression. Until these are given explicitly, it is not possible to answer the question.
1
The limit is 0.
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.
You can use the L'hopital's rule to calculate the limit of e5x -1 divided by sin x as x approaches 0.
limit x tends to infinitive ((e^x)-1)/(x)
1
The limit is 0.
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.
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.
You can use the L'hopital's rule to calculate the limit of e5x -1 divided by sin x as x approaches 0.
The limit is 4.
limit x tends to infinitive ((e^x)-1)/(x)
2
Take the limit of the top and the limit of the bottom. The limit as x approaches cos(2*90°) is cos(180°), which is -1. Now, take the limit as x approaches 90° of tan(3x). You might need a graph of tan(x) to see the limit. The limit as x approaches tan(3*90°) = the limit as x approaches tan(270°). This limit does not exist, so we'll need to take the limit from each side. The limit from the left is ∞, and the limit from the right is -∞. Putting the top and bottom limits back together results in the limit from the left as x approaches 90° of cos(2x)/tan(3x) being -1/∞, and the limit from the right being -1/-∞. -1 divided by a infinitely large number is 0, so the limit from the left is 0. -1 divided by an infinitely large negative number is also zero, so the limit from the right is also 0. Since the limits from the left and right match and are both 0, the limit as x approaches 90° of cos(2x)/tan(3x) is 0.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
9x/2x = 9/2 = 4.5
Yes, it does.