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Limits and Derivatives

Short Answer Type

91.

<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>

102 Views

92.

Find k if $stack space space space space space space lim with space space space space space space space space space straight x rightwards arrow 0 below space straight x space cosec space kx.$

97 Views

93.

Evaluate $space space space space space space space space space space limit as straight x rightwards arrow 0 to the power of minus of fraction numerator straight x over denominator open vertical bar straight x close vertical bar plus straight x squared end fraction$

103 Views

94.

Evaluate $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

112 Views

95.
Find the derivatives of followings functions from first principle.

(i) sin 2x (ii) cot (3x+1) $space space space space space space space space space space space space space space space left parenthesis iii right parenthesis space space space fraction numerator 1 over denominator square root of ax plus straight b end root end fraction$

(i) 2 cos 2x (ii) -3 cosec²(3x + 1) $space space space space space space space space space left parenthesis iii right parenthesis space minus straight a over 2 left parenthesis ax plus straight b right parenthesis to the power of negative 3 divided by 2 end exponent$

127 Views

96.

Find the derivative of sin²x from first principle.

122 Views

97.

Find the left and right derivatives of $space space space space space space space straight f left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 3 straight x comma end cell cell straight x less or equal than 1 end cell row cell 4 minus straight x comma end cell cell straight x greater than 1 end cell end table at space straight x space equals 1 close$

Find the left and that f is not differentiate at x = 1.

95 Views

98.

Differentiate following functions w.r.t. x

(i) x cosec x (ii) (1-2 tan x) (5 +4 sin x) (iii) x⁴tan x (iv) x sin x + cos x

115 Views

99.

Differentiate the following functions w.r.t. x.

$space space space space space space space space space space space space space space space space left parenthesis straight i right parenthesis space space space space fraction numerator left parenthesis straight x squared plus 1 right parenthesis left parenthesis straight x plus 3 right parenthesis over denominator straight x end fraction comma space straight x not equal to 0 space space space space space left parenthesis ii right parenthesis space space open parentheses straight x plus 1 over straight x close parentheses squared space space space space space space space space left parenthesis iii right parenthesis space space space fraction numerator 2 straight x plus 3 over denominator straight x squared minus 5 end fraction$