Book Store

Download books and chapters from book store.
Currently only available for.
CBSE

Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

91.

bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold lim with bold x bold rightwards arrow bold infinity below bold space fraction numerator bold log subscript bold e bold space bold left parenthesis bold 2 bold space bold plus bold space bold x bold right parenthesis bold space bold minus bold x to the power of bold 2 bold n end exponent bold sinx over denominator bold 1 bold space bold plus bold space bold x to the power of bold 2 bold n end exponent end fraction bold comma bold space bold ત ો bold space

$bold lim with bold x bold rightwards arrow bold 1 bold plus below$ f(x) નું અસ્તિત્વ નથી.
f(x) એ x = 1 અગળ સતત થાય.
$bold lim with bold x bold rightwards arrow bold 1 bold plus below$ f(x) = loge3.
$bold lim with bold x bold rightwards arrow bold 1 bold minus below$ f(x) = - sin 1.

92.

bold જ ો bold space bold lim with bold x bold rightwards arrow bold infinity below bold space open parentheses square root of bold x to the power of bold 6 bold space bold plus bold space bold ax to the power of bold 5 bold space bold equals bold space bold bx to the power of bold 3 bold space bold plus bold space bold cx bold space bold plus bold space bold d end root bold space bold minus bold space square root of bold x to the power of bold 6 bold space bold minus bold space bold 2 bold x to the power of bold 5 bold space bold plus bold space bold x to the power of bold 3 bold space bold minus bold space bold x bold space bold plus bold space bold 1 bold space end root close parentheses bold space bold equals bold space bold 2 bold comma bold comma bold space bold ત ો bold space

a = -2
b = -2
b = - 5
a = 2

93.

bold lim with bold e to the power of bold x bold rightwards arrow bold 1 end exponent below bold space open parentheses bold 4 over bold pi bold tan to the power of bold minus bold 1 end exponent bold x bold minus bold 1 close parentheses to the power of fraction numerator bold 1 over denominator bold x to the power of bold 2 bold minus bold 1 end fraction bold space end exponent bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

$bold e to the power of bold n bold space$
$bold e to the power of bold 2 over bold pi end exponent$
$bold e to the power of bold 1 over bold pi end exponent$
$bold space bold e to the power of fraction numerator bold minus bold 1 over denominator bold pi end fraction end exponent$

94. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell bold 1 bold plus bold x bold comma bold space end cell cell bold 0 bold less-than or slanted equal to bold x bold less-than or slanted equal to bold 2 end cell row cell bold 3 bold minus bold x bold comma bold space end cell cell bold 2 bold less than bold x bold less-than or slanted equal to bold 3 end cell end table close$ તો વિધેય f0f કેટલા બિંદુએ વિકલન ન થાય ?

95.

વિધેય g(x) એ વિધેય f(x) નું પ્રતિવિધેય છે. જો વિધેય f(x) એ R પર વિકલનીય હોય તો g"(f)x)) = .....

$fraction numerator bold f bold apostrophe bold left parenthesis bold x bold right parenthesis bold space bold f bold " bold left parenthesis bold x bold right parenthesis bold space bold minus bold space bold f bold left parenthesis bold x bold right parenthesis bold right parenthesis to the power of bold 2 over denominator bold f bold apostrophe bold left parenthesis bold x bold right parenthesis end fraction bold space bold space$
$fraction numerator bold f bold apostrophe bold left parenthesis bold x bold right parenthesis bold space bold f bold " bold left parenthesis bold x bold right parenthesis bold space bold minus bold space bold f bold left parenthesis bold x bold right parenthesis bold right parenthesis to the power of bold 2 over denominator bold left parenthesis bold f bold apostrophe bold left parenthesis bold x bold 0 bold right parenthesis to the power of bold 2 end fraction bold space$
$fraction numerator bold space bold f bold " bold left parenthesis bold x bold right parenthesis over denominator bold left parenthesis bold f bold apostrophe bold left parenthesis bold x bold right parenthesis bold right parenthesis to the power of bold 3 end fraction bold space bold space$
$fraction numerator begin display style bold minus bold f bold " bold left parenthesis bold x bold right parenthesis end style over denominator begin display style bold left parenthesis bold f bold apostrophe bold left parenthesis bold x bold right parenthesis bold right parenthesis to the power of bold 3 end style end fraction bold space bold space$

96.

ધારો કે વિધેય f એ દ્વિતિય વિકલિત ધરાવતું એવું વિધેય છે, જ્યાં f"(x) = -f(x) અને f'(x) = g(x). જો h(x) = (f(x))² + (g(x))² અને h(5) = 3 તો h(10) = .......

97. જો 5 f(x) + 3f $open parentheses bold 1 over bold x close parentheses$ = x + 2 અને y = x f(x), તો $open parentheses bold dy over bold dx close parentheses subscript bold x bold equals bold 1 end subscript bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.$

$bold 7 over bold 8$
14
-1
1

98.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open curly brackets table attributes columnalign left end attributes row cell bold a bold space bold plus bold space bold sin bold minus bold 1 bold space bold left parenthesis bold x bold space bold plus bold space bold b bold right parenthesis bold. bold space end cell row cell bold x bold comma bold space end cell end table close table row cell bold x bold greater than bold 1 end cell row cell bold x bold less than bold 1 end cell end table$ એ x = 1 આગળ વિકલનીય હોય, તો a = ........ , b = .....