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

Assignment Help:

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.


Related Discussions:- What is the limit of sin (1/x) when x tends to zero?

Maths For Fun, Ask Suppose I offer you a loan to start a safety matchstick ...

Ask Suppose I offer you a loan to start a safety matchstick production unit on the following terms: I shall first advance you Rs.50,000/- to set up your unit, and wait for 3 month

Sequencing model, theory about solving sequencing problem using graphical m...

theory about solving sequencing problem using graphical method

ConnectEd, How do I increase and decrease tax and sales

How do I increase and decrease tax and sales

What is pythagorean triples, What is Pythagorean Triples? A set of thre...

What is Pythagorean Triples? A set of three numbers a, b, and c that can satisfy the equation A 2 +b 2 = c 2 , is called a Pythagorean triple. The following is a list of

Calculate the area of rectangle , Calculate the area of RECTANGLE ? Th...

Calculate the area of RECTANGLE ? The area of a rectangle is the amount of space taken up by a rectangle, which is a two-dimensional shape. You find the area (A) of a recta

What is the continuously compounded forward rate, At time t an investor s...

At time t an investor shorts a $1 face value zero coupon bond that matures at time T = t and uses the entire proceeds to purchase a zero coupon bond that matures at time

Compute the total and annual return on the investment, 1. Calculate the ann...

1. Calculate the annual interest that you will receive on the described bond-A $500 Treasury bond with a current yield of 4 .2% that is quoted at 106 points? 2. Compute the tota

3/11/2013 7:23:14 AM

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

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd