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limx=>05x/(3sin(x)*cos(x)) = 5/3 * limx=>0(x/(sin(x)*cos(x)) = 5/3 * (1/limx=>02x)) = 5/3 * 1/1 = 5/3.
Another Summary:
As a start, you must remove the interdeterminant forms by using the L'Hopital rule:
Deriving the terms, we have:
5/3 * limx=>0(1/(cos2(x) - sin2(x)) = 5/3 * limx=>0(1/cos(2x))
Rule of Continuity:
5/3 * (1/cos(limx=>0(2x)) = 5/3 * 1/(cos(0)) = 5/3 * 1/1 = 5/3.
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What is 1 divided by infinity?
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.
What is calculus about?
Calculus is about applying the idea of limits to functions in various ways. For example, the limit of the slope of a curve as the length of the curve approaches zero, or the limit of the area of rectangle as its length goes to zero. Limits are also used in the study of infinite series as in the limit of a function of xas x approaches infinity.
Does limit always tend to zero only?
No, limit can tend to any finite number including 0. It is also possible that the limit does not tend to any finite value or approaches infinity. Example: The limit of x^2+5 tend to 6 as x approaches -1.
What is limit of 1 cos x divided by x as x approaches 0?
Undefined: You cannot divide by zero
What is the limit of x-sin x cos x over tan x -x as x tends to zero?
The limit is 2. (Take the deriviative of both the top and bottom [L'Hôpital's rule] and plug zero in.)
WHAT IS ZERO DIVIDE 0?
The ratio 0/0 is called "indeterminate" because it is defined in terms of the limit (as x ---> 0) of the numerator which we will write as n(x) divided by the limit (as x --->0) of the denominator which we will write as d(x). Now, If the numerator n(x) approaches zero faster than the denominator d(x), then the ratio is zero, but If d(x) approaches zero faster than n(x) then the ratio approaches infinity.
How many times does 0 divide into 10?
0
What is 1 divided by infinity?
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.
How do you solve the limit as x approaches 90 degrees of cos 2x divided by tan 3x?
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.
What is the limit of x as it approaches infinity for e to the negative 2x divided by the square root of 1-x squared?
1
Is zero divided by zero equal to zero?
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.
What is limit of 1 -cos x divided by x as x approaches 0?
1
What is calculus about?
Calculus is about applying the idea of limits to functions in various ways. For example, the limit of the slope of a curve as the length of the curve approaches zero, or the limit of the area of rectangle as its length goes to zero. Limits are also used in the study of infinite series as in the limit of a function of xas x approaches infinity.
What is the limit of sine squared x over x as x approaches zero?
So, we want the limit of (sin2(x))/x as x approaches 0. We can use L'Hopital's Rule: If you haven't learned derivatives yet, please send me a message and I will both provide you with a different way to solve this problem and teach you derivatives! Using L'Hopital's Rule yields: the limit of (sin2(x))/x as x approaches 0=the limit of (2sinxcosx)/1 as x approaches zero. Plugging in, we, get that the limit is 2sin(0)cos(0)/1=2(0)(1)=0. So the original limit in question is zero.
Why the number 0 has no reciprocal?
Division by zero is not allowed/defined. So you cannot take 'one over zero', or have zero in the denominator.Without going too technical, a person might say that 1/0 is infinity, and it sounds good. But if you have a function [say f(x) = 1/x] and take the limit of f(x) as x approaches zero, then f(x) approaches infinity as x approaches from the right, but it approaches negative infinity as you approach from the left, therefore the limit does not exist.
Does limit always tend to zero only?
No, limit can tend to any finite number including 0. It is also possible that the limit does not tend to any finite value or approaches infinity. Example: The limit of x^2+5 tend to 6 as x approaches -1.
Instantaneous speed is total distance traveled divided by total time of travel this is true and false?
False. Instantaneous speed is distance travelled divided by time, for a very short time interval. (Technically, you take the limit, when the time interval approaches zero.)
