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If f(x) cos(2x).cos(4x).cos(6x).cos(8x).cos(10x) then find the limit of 1 - f(x)35(sinx)2 as x tends to 0 (zero).?
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∙ 6y ago
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If f(x) = cos(2x).cos(4x).cos(6x).cos(8x).cos(10x) then,
find the limit of {1 - [f(x)]^3}/[5(sinx)^2] as x tends to 0 (zero).
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∙ 6y ago
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Find the limit of lim sin 4x sin 6x x 0?
Unfortunately, the browser used by Answers.com for posting questions is incapable of accepting mathematical symbols. This means that we cannot see the mathematically critical parts of the question. We are, therefore unable to determine what exactly the question is about and so cannot give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "divided by", "equals" etc. As it appears, you seem to be seeking the limit of sin(4x)*sin(6x) as x tends to 0. Both components of the product tend to 0 as x tens to 0 and so the limit is 0. Bit I suspect that is not the limit that you are looking for.
Limits in calculus?
A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.
Finding the limit in calculus?
To find the limit in calculus, you are trying to get as close as possible to the "real" answer of the problem.You are not actually finding the "true" answer of the problem, but rather the boundaries of the "limit" (infinity) of the number based on the lower limit, and upper limit of your graph. That's not true. Limits are a precisely defined concept. At least, if you know what the context is then they are. Since you mentioned calculus, I'm going to assume you're interested in the definition of a derivative. First, some notation. For any number x, the term |x| means the absolute value of x. So |3|=3, |-5|=5, |-2.7|=2.7, |7.8|=7.8, etc. Suppose f:R->R. Then f'(p), the derivative of f at p (if it exists) is defined as: lim { (f(p+h)-f(p))/h }h->0 What does this actually mean? The intuition is this: the smaller h is, the closer (f(p+h)-f(p))/h gets to the derivative.* We say (f(p+h)-f(p))/h tends to f'(p) as h tends to 0. In other words, we can make the difference| { (f(p+h)-f(p))/h } - f'(p) |as small as we want, just by forcing h to be small. More formally: For any positive real number e, there is a positive real d such that, for any real h with |h| | { (f(p+h)-f(p))/h } - f'(p) | < e. The derivative f'(p) is defined as the only real number with this property. You can never have more than one number with this property. There might not be any, in which case the function f is not differentiable at p.* The intuition here is as follows: (p+h,f(p+h)) is a point on the curve close to (p,f(p)), the point we are interested in. The line between these points (let's call it L) is almost the same as the tangent to the curve (T), and its gradient is almost the gradient of the tangent (which is the derivative). But the gradient of L is(f(p+h)-f(p))/hand therefore this quantity is close to f'(p). Another way Think about a curve on a sheet of paper on a X-Y graph. If you are interested in the point, say x = a, and you follow the curve from the left of the point going toward the point x=a and arrive at some value, say C, then you follow the curve from the right going toward the point x=a and arrive at a point, again C, then the limit of the function as x->a = c so to find the limit, the limit FROM THE LEFT and the limit FROM THE RIGHT both have to have the same value if lim x-> a of f(x) from the left = lim x -> a of f(x) from the right, and both limits = C then lim x -> a of f(x) = C
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