Book Store

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

Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

21.

bold lim with bold x bold rightwards arrow bold infinity below bold space bold x bold space bold sum from bold i bold space bold equals bold space bold 1 to bold n of open parentheses fraction numerator bold 1 over denominator bold e to the power of bold x bold minus bold 1 end fraction close parentheses bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

$fraction numerator bold n to the power of bold 2 bold left parenthesis bold n bold plus bold 1 bold right parenthesis to the power of bold 2 over denominator bold 4 end fraction$
$fraction numerator bold n bold plus bold 1 over denominator bold 2 end fraction bold space$
$fraction numerator bold n to the power of bold 2 bold plus bold 1 over denominator bold 2 end fraction$
$fraction numerator bold n bold left parenthesis bold n bold plus bold 1 bold right parenthesis over denominator bold 2 end fraction$

22.

bold જ ો bold space bold space bold 3 bold f bold left parenthesis bold x bold right parenthesis bold space bold minus bold space bold 2 bold space bold f open parentheses bold 1 over bold x close parentheses bold space bold equals bold space bold x bold space bold હ ો ય bold space bold ત ો bold space bold f bold apostrophe bold left parenthesis bold 2 bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space

$bold 1 over bold 2$
$fraction numerator begin display style bold 2 end style over denominator begin display style bold 7 end style end fraction$
$bold 7 over bold 2$
2

23.

જો f(x) = p |sin x| + qe^|x| + r|x|³ એ x = 0 આગળ વિકલનીય હોય તો.........

q = 0, r = 0, p ∈ R
r = 0, p = 0, q ∈ R
p + q = 0, p ∈ R
q + r = 0, p∈ R

24.

bold lim with bold n bold rightwards arrow bold infinity below bold space bold cos bold space bold x over bold 2 bold space bold cos bold space bold x over bold 4 bold space bold cos bold space bold x over bold 8 bold space bold. bold. bold. bold. bold. bold space bold cos bold space bold x over bold 2 to the power of bold n bold space bold space bold. bold. bold. bold. bold. bold. bold. bold space

$Error converting from MathML to accessible text.$
$Error converting from MathML to accessible text.$
sin x
cos x

25.

જો $bold tan bold space bold y over bold 2 bold space bold equals bold space fraction numerator square root of bold 1 bold minus bold e end root over denominator square root of bold 1 bold plus bold e end root end fraction bold space bold tan bold space bold x over bold 2 bold space bold ત ો bold space bold dy over bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold.$

$square root of fraction numerator bold 1 bold minus bold e to the power of bold 2 over denominator bold 1 bold plus bold e bold space bold cosx end fraction end root$
$fraction numerator square root of bold 1 bold plus bold e to the power of bold 2 end root over denominator bold 1 bold space bold plus bold space bold e bold space bold cosx end fraction$
$fraction numerator square root of bold 1 bold space bold minus bold space bold e to the power of bold 2 end root over denominator bold 1 bold space bold minus bold space bold e bold space bold cosx end fraction$
$fraction numerator square root of bold 1 bold minus bold e end root to the power of bold 2 over denominator bold 1 bold plus bold e bold space bold cosx to the power of bold 2 end fraction$

26.

bold જ ો bold space bold y bold space bold equals bold space bold tan bold minus bold 1 bold space open parentheses fraction numerator bold log bold space bold e bold space bold x to the power of bold minus bold 2 end exponent over denominator bold log bold space bold e bold space bold x to the power of bold 2 end fraction close parentheses bold space bold plus bold space bold tan to the power of bold minus bold 1 end exponent bold space open parentheses fraction numerator bold 3 bold plus bold 2 bold space bold log bold space bold x over denominator bold 1 bold space bold minus bold space bold 6 bold space bold log bold space bold x end fraction close parentheses bold space bold ત ો bold space bold dy over bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.

27.

bold lim with bold x bold rightwards arrow bold 0 below bold space fraction numerator bold 1 bold space bold minus bold space bold cos bold left curly bracket bold 1 bold space bold minus bold space bold cos bold space bold left parenthesis bold space bold 1 bold space bold minus bold space bold cosθ bold right parenthesis bold right curly bracket bold space over denominator bold theta to the power of bold 8 end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

$bold 1 over bold 4$
$bold 1 over bold 16$
$bold 1 over bold 64$
$bold 1 over bold 128$

bold 1 over bold 128

Tips: -

bold આપણ ે bold space bold ન ોં ધ ી એ bold space bold ક ે bold space bold space bold lim with bold x bold rightwards arrow bold 0 below bold space fraction numerator bold 1 bold space bold minus bold space bold cosx over denominator bold x to the power of bold 2 end fraction bold space bold equals bold space bold 1 over bold 2 bold હવ ે bold space bold મ ાં ગ ે લ bold space bold લક ્ ષ bold space bold space bold space bold lim with bold x bold rightwards arrow bold 0 below bold space bold equals bold space fraction numerator bold 1 bold minus bold cos bold left curly bracket bold 1 bold minus bold cos bold left parenthesis bold 1 bold minus bold cosθ bold right parenthesis bold right curly bracket over denominator bold left curly bracket bold 1 bold minus bold cos bold left parenthesis bold 1 bold minus bold cosθ bold right parenthesis bold right curly bracket to the power of bold 2 end fraction bold space bold cross times bold space fraction numerator bold left curly bracket bold 1 bold minus bold cos bold left parenthesis bold 1 bold minus bold cosθ bold right parenthesis bold right curly bracket over denominator bold left parenthesis bold 1 bold minus bold cosθ bold right parenthesis to the power of bold 4 end fraction bold space bold cross times bold space fraction numerator bold left parenthesis bold 1 bold minus bold cosθ bold right parenthesis to the power of bold 4 over denominator bold theta to the power of bold 8 end fraction bold જ ે મ bold space bold theta bold rightwards arrow bold 0 bold space bold ત ે મ bold space bold 1 bold space bold minus bold space bold cos bold space bold theta bold space bold rightwards arrow bold space bold અન ે bold space bold 1 bold space bold minus bold space bold cos bold space bold left parenthesis bold 1 bold space bold minus bold space bold cosθ bold right parenthesis bold space bold rightwards arrow bold space bold 0 bold left parenthesis bold 1 bold right parenthesis bold space bold ન ો bold space bold ઉપય ો ગ bold space bold કરત ાં bold comma bold space bold મ ાં ગ ે લ bold space bold લક ્ ષ bold space bold equals bold space bold 1 over bold 2 bold space open parentheses bold 1 over bold 2 close parentheses to the power of bold 2 bold space open parentheses bold 1 over bold 2 close parentheses to the power of bold 2 bold space bold equals bold space bold 1 over bold 128

28.

bold x bold space square root of bold 1 bold plus bold x end root bold space bold plus bold space bold y bold space square root of bold 1 bold plus bold y end root bold space bold equals bold space bold 0 bold space bold મ ા ટ ે bold space bold dy over bold dx bold space bold equals bold space bold. bold comma bold. bold. bold. bold. bold. bold. bold. bold space

$fraction numerator bold 1 over denominator bold left parenthesis bold 1 bold plus bold x bold right parenthesis to the power of bold 2 end fraction bold space$
$fraction numerator bold 1 over denominator bold 1 bold plus bold x to the power of bold 2 end fraction bold space$
$fraction numerator bold minus bold 1 over denominator bold 1 bold plus bold x to the power of bold 2 end fraction bold space$
$fraction numerator bold minus bold 1 over denominator bold 1 bold plus bold x bold right parenthesis to the power of bold 2 end fraction$

29.

bold જ ો bold space bold space bold y bold space bold equals bold space fraction numerator bold 1 over denominator square root of bold cos bold space bold 2 bold x end root end fraction bold space bold ત ો bold space bold y to the power of bold 2 bold space bold plus bold space bold y bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space

y⁵
2y⁵
3y⁵
4y⁵

30.

જો x = sec θ - cis θ અને y - secⁿθ - cosⁿ θ, તો (x² + 4) $open parentheses bold dy over bold dx close parentheses to the power of bold 2$ = ......... (y² + 4)

Switch

Book Store

Subject

Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

Switch