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Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

31.

જો વિધેય f એ R પર સતત છે તથા $bold f open parentheses fraction numerator bold 1 over denominator bold 4 bold n end fraction close parentheses bold space bold equals bold space bold left parenthesis bold sin bold space bold e to the power of bold n bold right parenthesis bold space bold e to the power of bold minus bold n to the power of bold 2 end exponent bold space bold plus bold space fraction numerator bold n to the power of bold 2 over denominator bold n to the power of bold 2 bold space bold plus bold space bold 1 end fraction bold space bold ત ો bold space bold f bold left parenthesis bold 0 bold right parenthesis bold space bold space$ ની કિંમત .....

0
-1
1
$bold 1 over bold 2$

32. જો x = f(t), y = g(t), y = g(t) તો $fraction numerator bold d to the power of bold 2 bold y over denominator bold dx to the power of bold 2 end fraction$ = ........

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

33. f(x) = $fraction numerator bold 1 over denominator bold log bold space bold vertical line bold x bold vertical line end fraction$ એ કેટલાં બિંદુઓએ અસતત થશે ?

34.

bold જ ો bold space bold y bold space bold equals bold space fraction numerator bold ax to the power of bold 2 over denominator bold left parenthesis bold x bold space bold minus bold space bold a bold right parenthesis bold space bold left parenthesis bold x bold space bold minus bold space bold b bold right parenthesis bold space bold left parenthesis bold x bold space bold minus bold space bold c bold right parenthesis bold space end fraction bold space bold plus bold space fraction numerator bold bx over denominator bold left parenthesis bold x bold space bold minus bold space bold b bold 0 bold space bold left parenthesis bold x bold space bold minus bold space bold c bold right parenthesis bold space end fraction bold space bold plus bold space fraction numerator bold c over denominator bold x bold space bold minus bold space bold c end fraction bold space bold plus bold space bold 1 bold space bold ત ો bold space bold y over bold y bold space bold equals bold space bold. bold. bold. bold. bold.

$Error converting from MathML to accessible text.$
$bold 1 over bold 2 open parentheses fraction numerator bold a over denominator bold a bold minus bold x end fraction bold plus fraction numerator bold b over denominator bold b bold minus bold x end fraction bold plus fraction numerator bold c over denominator bold c bold minus bold x end fraction close parentheses bold space$
$Error converting from MathML to accessible text.$
$bold 1 over bold x$

35.

$bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold tan bold left square bracket bold e to the power of bold 2 bold right square bracket bold space bold minus bold space bold tan bold left square bracket bold minus bold e bold right square bracket bold x to the power of bold 3 over denominator bold sin to the power of bold 3 bold x end fraction bold comma bold space$ x # 0. જો f એ x = 0 આગળ સતત હોય તો f(0) = .....

36.

bold જ ો bold space bold space bold f bold left parenthesis bold x bold right parenthesis bold space open curly brackets table row cell bold left parenthesis bold 1 bold plus bold vertical line bold sin bold space bold x bold vertical line to the power of fraction numerator bold a over denominator bold vertical line bold sin bold space bold x bold vertical line end fraction end exponent end cell cell fraction numerator bold minus bold pi over denominator bold 6 end fraction bold less than bold x bold less than bold 0 end cell row bold b cell bold x bold space bold equals bold space bold 0 bold space end cell row cell bold e to the power of bold tan bold 2 bold x bold µ bold tan bold 3 bold x end exponent end cell cell bold 0 bold space bold less than bold space bold x bold space bold less than bold space bold pi over bold 6 end cell end table close bold space bold એ bold space open parentheses fraction numerator bold minus bold pi over denominator bold 6 end fraction bold comma bold pi over bold 6 close parentheses bold space bold પર bold space bold સતત bold space bold હ ો ય bold space bold ત ો bold comma bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space

$bold a bold space bold equals bold space bold 2 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 2 bold space bold space$
$bold space bold a bold space bold equals bold space bold 1 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 1 over bold 3 end exponent bold space$
$bold a bold space bold equals bold space bold e to the power of bold 1 over bold 2 end exponent bold comma bold space bold b bold space bold equals bold e bold space to the power of bold 2 over bold 3 end exponent bold space bold space$
$bold space bold a bold space bold equals bold space bold 2 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 2 over bold 3 end exponent$

37.

y = xⁿ (a cos (log x) + b sin (log x)). જો y એ x²y₂ + (1 - 2n) xy, + ay = 0 નું સમાધાન કરે તો A = .......

n
1 - n²
1 + n²
$bold 1 bold plus bold 1 over bold n$

1 + n²

Tips: -

y = xⁿ(a cos (log x) + b sin (log x))

y₁ = nx^n-1 (a cos (log x) + b cos (log x)) + xⁿ

xy₁ = ny + xⁿ (-a sin (log x) + b cos (log x))

xy₂ + y₁ = ny₁ + nx^n-1 (-a sin (log x) + b cos (log x)) + xⁿ (-a cos(log x) $bold 1 over bold x$ -b sin (log x) $bold 1 over bold x$ )

x²y₂ + xy₁ = nxy₁ + n (xy₁ - ny) - y

x²y₂ + (1 - 2n) xy₁ + (1 + n²)y = 0

38.

f(x) = $fraction numerator bold 1 over denominator bold 1 bold minus bold x end fraction$ g(x) = f³ⁿ(x) જ્યાં fⁿ(x) = fofof ..... of (n વખત). વિધેય g(x) કેટલા બિંદુએ અસતત થશે ?

2ન
3n
2
2n + 1

39.

f અને g વિકલનીય વિધેય છે. g'(a) = 2. g(a) = b તથા fog = I તો f'(b) = ........

1
2
$bold 2 over bold 3$
$bold 1 over bold 2$

40. જો f(x) = $bold x over bold 2 bold minus bold 2$ તો અંતરાલ $bold left square bracket bold 0 bold comma bold space bold pi bold right square bracket$ પર

tan (f(x)) અને f^-1(x) બંને સતત થશે.
tan (f(x)) અને f^-1(x) બંને અસતત થશે.
tan (f(x)) અને $fraction numerator bold 1 over denominator bold f bold left parenthesis bold c bold right parenthesis end fraction$ બંને સતત થશે.
tan (f(x)) અને $fraction numerator bold 1 over denominator bold f bold left parenthesis bold c bold right parenthesis end fraction$ બંને અસતત થશે.

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Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

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