Maths, continuity

Plz help me out with a solution...

f(x) = sin(1/x)
when x is not = to 0 and f(0) = 0

A function is continuous if
Limit of y-->x of f(y) equals f(x) for every x. In this case you have t see if this is the case for x = 0. f(0) = 0, therefore we need to calculate:

Limit x--->0 f(x)

It turns out that this limit does not exist, therefore the function is not continuous. However, for this problem you only need to show that the limit cannot be equal to zero.

Suppose the limit is zero, then for every interval I from minus delta to plus delta you can always find an epsilon such that the function maps the interval ranging from -epsilon to plus epsion into the interval I. So, you can make delta arbitrarily small and still find a range around zero that is mapped by f to I.

In this case this is clearly not true. The function oscillates between minus 1 and 1 for arbitrary small values of x. This means that for delta smaller than one, there is no interval containing zero which will be mapped by f to the range from minus delta to delta, because any interval containing zero, no matter how small, is mapped by f to an interval ranging from minus 1 to 1.

1. 👍 0
2. 👎 0
3. 👁 67

Similar Questions

1. calculus help plllllz

if you go with the right substitution ∫[{(1-sin(x))/(1+sin(x))}{(2-sin(x))/(2+sin(x))}] dx plz show me solution

asked by rapheal on September 26, 2016
2. calculus-help me sir~steve

show that 2f''(t)-f'(t)-f(t)=sin(t)-cos(t) where f(0)=f'(0) has the solution (-2/5)e^(-t/2)-(1/5)sin(t)+(2/5)cos(t) using laplace tranformation plz plz plz show step by step

asked by dam on May 26, 2016
3. Calculus

I need to find the exact solutions on the interval [0,2pi) for: 2sin^2(x/2) - 3sin(x/2) + 1 = 0 I would start: (2sin(x/2)-1)(sin(x/2)-1) = 0 sin(x/2)=1/2 and sin(x/2)=1 what's next? Ok, what angle has a sin equal to say 1/2 sin

asked by Jen on August 21, 2006
4. math

Which ordered pair is not a solution of y = -12x - 3? a. (-3,33)* b. (8,-98) c.(-9, 105) d.(3,-39) plz check plz plz plz plz plz

asked by alabama joe on March 15, 2019
5. trigonomentry prove

[sin(b)+sin(2b)]/(1+cosb+sin(2b)=tanb plz i need ur help prove for me show step

asked by nuru on April 12, 2017
6. math

Determine all the possible values of x where 0 deg is more than or equal to x and x is more or equal to 360 deg such that i'm not sure the solution, please correct it, sin x sec x - 3 sin x = 0 the solution: sin x 1/cos x - 3 sin

asked by choi2463 on April 15, 2013
7. TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

asked by hayden on February 23, 2009
8. LIVING ENVIRONMENT

the ability to grow in size is a characteristic of living organism .Although an icicle may grow in size over time,it is considered nonliving because there is 1)an incerase in matter ,but no increase in the number of icicle. 2)an

asked by tania sharmin on February 12, 2013
9. Math

-14+26-37-45+56-67-71. ___? i don't know how to solve this so plz tell me this with solution. -12-(-24)+(-36) my answer is 0 but its wrong i cant understand tell me this with solution plz. Thanks

asked by purplemath on October 9, 2009
10. Math

|(sin(x + p), sin(x + q), sin(x + r)), (sin(y + p), sin(y + q), sin(y + r)), (sin(z + p), sin(z + q), sin(z + r))| Please help me with full solution have done all i could No hint please just help me please please

asked by Dema on July 10, 2019
11. maths sir damon reiny or steve help!steve see

Given u(x, y) = x^2 + 2y where x (r, t) = r sin(t) and y(r,t) = sin^2(t), determine the value of ∂u / ∂r and ∂u / ∂t using the chain rule. Plz show step

asked by payuto on March 15, 2017

More Similar Questions