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CBSE

Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

41.

bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold 2 to the power of bold x bold minus bold 1 over denominator square root of bold 1 bold plus bold ax end root bold minus bold 1 end fraction bold space bold અન ે 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 log subscript bold e bold space bold 4 bold comma bold space bold ત ો bold space bold a bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space

1
log_e 2-1
log_e 2 + 1
log_e 2

42.

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) = ......

43.

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
$bold 1 over bold e$

44.

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

bold 1 over bold 2

Tips: -

bold lim with bold h bold rightwards arrow bold 0 below bold space fraction numerator bold f bold left parenthesis bold 2 bold plus 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 minus 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 lim with bold h bold rightwards arrow bold 0 below bold space fraction numerator bold f bold apostrophe bold left parenthesis bold 2 bold space bold plus bold space bold h to the power of bold 2 bold right parenthesis bold 2 bold h bold minus bold f bold left parenthesis bold 2 bold minus bold h to the power of bold 2 bold right parenthesis bold left parenthesis bold minus bold 2 bold h bold right parenthesis over denominator bold 4 bold h end fraction bold equals bold space bold lim with bold h bold rightwards arrow bold 0 below bold space fraction numerator bold f bold apostrophe bold left parenthesis bold 2 bold plus bold h to the power of bold 2 bold right parenthesis bold plus bold f bold apostrophe 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 end fraction bold space bold equals bold space bold f bold apostrophe bold left parenthesis bold 2 bold right parenthesis bold space bold equals bold space bold 1

45. 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 ..............