Evaluate the following :
<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>


space space space space space limit as space space straight x rightwards arrow negative 1 of left parenthesis 1 plus straight x plus straight x squared plus...... space plus space straight x squared right parenthesis space equals stack lim space space left parenthesis 1 right parenthesis with straight x rightwards arrow negative 1 below plus limit as straight x rightwards arrow negative 1 of left parenthesis straight x right parenthesis space plus space limit as straight x rightwards arrow negative 1 of straight x squared plus space...... plus space limit as straight x rightwards arrow negative 1 of straight x to the power of 12

        = 1 + (-1) + (-1)2 + .... + (-1)12 = 1 + (-1) + 1 + ..... + 1 = 1
327 Views

Evaluate the following :
space space space space space space space limit as straight x rightwards arrow of left parenthesis 3 minus straight x squared right parenthesis


space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 1 of left parenthesis 3 minus straight x squared right parenthesis space equals limit as straight x rightwards arrow 1 of 3 minus limit as straight x rightwards arrow 1 of straight x squared equals 3 minus left parenthesis 1 right parenthesis squared equals 3 minus 1 equals 2
575 Views

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.


Evaluating the funtion at x =2, it is of the form <pre>uncaught exception: <b>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</b><br /><br />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<br />#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

207 Views

Evaluate     <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>.


Evaluating the function at x =2, it is of the form space 0 over 0.
Therefor, space space space space space space space space space 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 straight x cubed minus 4 straight x squared plus 4 straight x over denominator straight x squared minus 4 end fraction equals limit as straight x rightwards arrow 2 of fraction numerator straight x left parenthesis straight x squared minus 4 straight x plus 4 right parenthesis over denominator straight x squared minus 2 squared end fraction equals limit as straight x rightwards arrow 2 of fraction numerator straight x left parenthesis straight x minus 2 right parenthesis squared 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 straight x left parenthesis straight x minus 2 right parenthesis over denominator straight x plus 2 end fraction

                                                                                                                                                                                                                                                                                                                                                          space space space space space space space space space space space space space space space space space space space space space open parentheses because space straight x not equal to 2 rightwards double arrow negative 2 not equal to 0 close parentheses
          space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 3 left parenthesis 2 right parenthesis plus 5 over denominator 2 plus 2 end fraction equals 11 over 4
214 Views

Evaluate the following :
<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>


space space space space space space space space space space space space space space space limit as straight x rightwards arrow 4 of left square bracket straight x left parenthesis straight x plus 1 right parenthesis right square bracket space equals space open parentheses limit as straight x rightwards arrow 4 of space straight x close parentheses. open parentheses limit as straight x rightwards arrow 4 of left parenthesis straight x plus 1 right parenthesis close parentheses equals 4 open parentheses limit as straight x rightwards arrow 4 of straight x plus limit as straight x rightwards arrow 4 of 1 close parentheses equals 4 left parenthesis 4 plus 1 right parenthesis equals 4 left parenthesis 5 right parenthesis equals 20
318 Views