Evaluate $space space space space space space space space space space space space space space stack space lim with straight x rightwards arrow 3 below fraction numerator 3 straight x squared minus straight x minus 10 over denominator straight x squared minus 4 end fraction.$

Answer

Evaluating the funtion at x =2, it is of the form $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ .
Therefore, $space space space space space space space space space space space space space space space limit as straight x rightwards arrow 2 of fraction numerator 3 straight x squared minus straight x minus 10 over denominator straight x to the power of 2 straight x end exponent minus 4 end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 3 straight x squared minus 6 straight x plus 5 straight x plus 10 over denominator straight x squared minus 2 squared end fraction equals limit as straight z rightwards arrow 2 of fraction numerator left parenthesis straight x minus 2 right parenthesis left parenthesis 3 straight x plus 5 right parenthesis over denominator left parenthesis straight x minus 2 right parenthesis left parenthesis straight x plus 2 right parenthesis end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 3 straight x plus 5 over denominator straight x plus 2 end fraction$

 $space space space space space space space space space open square brackets because space straight x space not equal to 2 rightwards double arrow straight x minus 2 not identical to 0 close square brackets$
 $space space space space space space space space equals space space fraction numerator 2 left parenthesis 2 minus 2 right parenthesis over denominator 2 plus 2 end fraction equals fraction numerator 2 left parenthesis 0 right parenthesis over denominator 4 end fraction equals 0$