Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Limits and Derivatives

Short Answer Type

31.

Let f(x) $space space space space space equals space open curly brackets table attributes columnalign left end attributes row cell 1 minus straight x squared comma space straight x less or equal than 0 end cell row cell 1 plus straight x squared comma space straight x space greater than 0 end cell end table close$ find Lf'(0) and Rf'(0)

Is f derivable at x = 0?

97 Views

32. Find the derivative of the function f(x) = 99x at x= 100.

205 Views

33.

Let $space space space straight f left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell straight x plus straight a comma space straight x less or equal than 1 end cell row cell ax squared plus 1 comma space straight x greater than 1 end cell end table close$

find a so that f may be derivable at x =1.

92 Views

34.

If f is derivable at x=a, evaluate $space space space space space space space space space stack space lim with straight x rightwards arrow straight a below fraction numerator xf left parenthesis straight a right parenthesis minus af left parenthesis straight x right parenthesis over denominator straight x minus straight a end fraction$ .

99 Views

35.

For the function :

$space space space space space space space space straight f left parenthesis straight x right parenthesis space equals straight x to the power of 100 over 100 plus straight x to the power of 99 over 99 plus.... plus fraction numerator straight x squared 2 over denominator 2 end fraction plus straight x plus 1$ Prove that f(1) = 100 f'(0)

116 Views

36. For some constants a and b, find the derivatives of the following functions :

(x-a)(x-b)

103 Views

37. For some constants a and b, find the derivatives of the following functions :

(ax²+b)²

109 Views

38. For some constants a and b, find the derivatives of the following functions :

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

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

$rightwards double arrow$ $space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx open parentheses fraction numerator straight x minus over denominator straight x minus straight b end fraction close parentheses equals fraction numerator left parenthesis straight x minus straight b right parenthesis begin display style straight d over dx end style left parenthesis straight x minus straight a right parenthesis minus left parenthesis straight x minus straight a right parenthesis begin display style straight d over dx end style left parenthesis straight x minus straight b right parenthesis over denominator left parenthesis straight x minus straight b right parenthesis squared end fraction$

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space straight d over dx open parentheses straight u over straight v close parentheses equals fraction numerator straight v begin display style straight d over dx end style straight u minus straight u begin display style straight d over dx end style straight v over denominator straight v squared end fraction close square brackets$

$space space space space space space space space space space space space equals space fraction numerator left parenthesis straight x minus straight b right parenthesis left parenthesis 1 minus 0 right parenthesis minus left parenthesis straight x minus straight a right parenthesis left parenthesis 1 minus 0 right parenthesis over denominator left parenthesis straight x minus straight b right parenthesis squared end fraction space equals space fraction numerator straight x minus straight b minus straight x plus straight a over denominator left parenthesis straight x minus straight b right parenthesis squared end fraction equals fraction numerator straight a minus straight b over denominator left parenthesis straight x minus straight b right parenthesis squared end fraction$

109 Views

39. Find the derivative of the following :

(5x³+3x+1)(x-1)

144 Views

40. Find the derivative of the following :

x^-4 (3 - 4x^-5)

119 Views