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CBSE

Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

41.

bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open curly brackets fraction numerator bold log bold left parenthesis bold 1 bold _x bold right parenthesis to the power of bold 1 bold plus bold x end exponent over denominator bold x to the power of bold 2 end fraction bold minus bold 1 over bold x close curly brackets bold space bold ત ો bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

0
1
$bold 1 over bold 2$
$bold 1 over bold 4$

42.

bold lim with bold x bold rightwards arrow bold 0 below bold space bold x to the power of bold 7 bold space open square brackets bold 1 over bold x to the power of bold 3 close square brackets bold space bold equals bold space bold. bold. bold. bold. bold.

0
1
-1
અસ્તિત્વ નથી.

43.

bold જ ો bold space bold f bold apostrophe bold left parenthesis bold 2 bold right parenthesis bold space bold equals bold space bold 1 bold space bold ત ો bold space bold lim with bold x bold rightwards arrow bold 0 below bold space fraction numerator bold f bold left parenthesis bold 2 bold space bold plus bold space bold h to the power of bold 2 bold right parenthesis bold space bold minus bold space bold f bold left parenthesis bold 2 bold space bold minus bold space bold h to the power of bold 2 bold right parenthesis over denominator bold 2 bold h to the power of bold 2 end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space

1
$bold 1 over bold 2$
2
0

44.

bold વ િ ધ ે ય bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold x bold space fraction numerator bold e to the power of bold left square bracket bold x bold right square bracket bold plus bold vertical line bold x bold vertical line end exponent bold space bold minus bold space bold 2 over denominator bold left square bracket bold x bold right square bracket bold space bold plus bold space bold vertical line bold x bold vertical line bold space end fraction bold space bold હ ો ય bold space bold ત ો bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

0
1
-1
અસ્તિત્વ નથી.

અસ્તિત્વ નથી.

Tips: -

bold minus bold 1 bold space bold less than bold space bold x bold space bold less than bold space bold 0 bold space bold મ ા ટ ે bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold space bold x bold space fraction numerator bold e to the power of bold minus bold 1 bold minus bold x end exponent bold minus bold 2 over denominator bold minus bold 1 bold minus bold 2 end fraction bold space bold equals bold space bold 0 bold space bold 0 bold space bold x bold space bold less than bold space bold 1 bold space bold મ ા ટ ે bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold space bold equals bold space bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold x bold space fraction numerator bold e to the power of bold minus bold 1 bold minus bold x end exponent bold minus bold 2 over denominator bold x end fraction bold space bold equals bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold e to the power of bold x bold minus bold space bold 2 bold space bold equals bold space bold minus bold 1 bold lim with bold x bold rightwards arrow bold 0 below bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold ન ું bold space bold અસ ્ ત િ ત ્ વ bold space bold નથ ી bold.

45.

bold lim with bold x bold rightwards arrow bold 0 below bold space open square brackets bold tan bold space open parentheses bold x over bold 4 bold space bold _ bold space bold x bold right parenthesis close parentheses close square brackets to the power of bold 1 over bold x end exponent bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space

e
e²
e^-2
$bold 1 over bold e$

46.

શૂન્યેત્તર વિધેય f એ f(x-y) = $fraction numerator bold f bold left parenthesis bold x bold right parenthesis over denominator bold f bold left parenthesis bold y bold right parenthesis end fraction$ પ્રકારનું છે. જો f'(0) = 5 અને f'(5) = 5, to f(5) = ......

47. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open curly brackets table attributes columnalign left end attributes row cell bold vertical line bold x bold vertical line bold comma end cell row cell bold left square bracket bold x bold right square bracket bold comma end cell end table close table row cell bold x bold less-than or slanted equal to bold 2 end cell row cell bold x bold greater than bold 2 end cell end table$ તો ..............