​Is the following function continous at the origin g(x,y)= siny* (2xy/(x^2+y^2

Anonymous
timer Asked: Jul 3rd, 2014
account_balance_wallet $5

Question Description

help me dear

Tutor Answer

khakaan
School: University of Maryland

Use \varepsilon -\delta definition to check continuity:

Let \varepsilon>0 be given.can we find \delta>0 such that if

 0<p><strong>  then</strong></p><p><strong> [img alt=we know that

[img alt="xy

because

 [img alt="-1\leq sinx\leq1" src="http://latex.codecogs.com/gif.latex?-1%5Cleq%20sinx%5Cleq1" >

then we can write

 xysiny<p><strong>that is</strong></p><p><strong> [img alt=

we have

 |f(x,y)-0|=\left | \frac{2xysiny}{x^{2}+y^{2}} \right |=2\left | \frac{xysiny}{x^{2}+y^{2}} \right |\leq 2\epsilon

so

\delta =2\epsilon will work.

therefore it is continous at (0,0)


flag Report DMCA
Review

Anonymous
Top quality work from this guy! I'll be back!

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors