What is the limit of sin (1/x) when x tends to zero?, Mathematics

As x tends to zero the value of 1/x tends to either ∞ or -∞. In this situation we will not be sure about the exact value of 1/x. As a result we will not be sure about the exact/approaching value of sin(1/x). We cant say anything about the value of sine function unless we know the angle and in this question we are not sure about the angle as at infinity it can take any value. We will be sure that the value of sin(1/x) will lie in [-1, 1] but not sure about a unique value. As in limits, it exists only when we get a unique value. Therefore we will say that the limit does not exist.

Posted Date: 3/11/2013 7:22:25 AM | Location : United States

Limit sin(1/x) when x tends to 0 is not defined

Can be proved simply by multiplying and dividing by x then xsin(1/x)/x becomes 1/x as xsin(1/x)or for that matter sin(1/x)/1/x = 1 and limit reduces to 1/x which doesnt exist

Also the proof can be that when x approcashes 0 from positive side 1/x tends to positive infinty and limit (right0 becomes sin(infinity) but when from left side 1/x tends to negative infinty so limit becomes -sin(infinit) which both can never b equal.

so limit doesnt exist

Posted by | Posted Date: 3/11/2013 7:23:14 AM

Related Discussions:- What is the limit of sin (1/x) when x tends to zero?, Assignment Help, Ask Question on What is the limit of sin (1/x) when x tends to zero?, Get Answer, Expert's Help, What is the limit of sin (1/x) when x tends to zero? Discussions

Write discussion on What is the limit of sin (1/x) when x tends to zero?
Your posts are moderated
Related Questions
David invests $17,000 into an account and at the end of 7 years, his account has a balance of $ 26,417.77. What is the interest rate (assuming annual compounding)?

Above we have seen that (2x 2 - x + 3) and (3x 3 + x 2 - 2x - 5) are the factors of 6x 5 - x 4 + 4x 3 - 5x 2 - x - 15. In this case we are able to find one facto

how to find value of cos20 without using calculator

Greatest Common Factor The primary method for factoring polynomials will be factoring the greatest common factor. While factoring in general it will also be the first thing

What is Permutations explain with examples? Each arrangement of a set of elements is called a permutation. In other words, every possible way (order) of writing a group of lett

AFIGURE THIS OUT(3) (14) (17) (20) (25)= 8 WHAT ARE THE PROCEDURES (-)(+)(x)(div) BETWEEN EACH NUMBER TO COME UP WITH 8 ?sk question #Minimum 100 words accepted#

Three mixtures were prepared with very narrow molar mass distribution polyisoprenesamples with molar masses of 8000, 25,000, and 100,000 as indicated below. (a) Equal numbers of

Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin

Here, we have tried to present some of the different thinking and learning processes of preschool and primary school children, in the context of mathematics learning. We have speci

Two boats leave the same port at the same time. One travels at a constant speed of 30 km/hr at a bearing of 50° and the other on a bearing of 110° at a constant speed of 26 km/hr.