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  • DLS

limits(38)

Mathematics
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  • hba
lol wut?
  • DLS
Let \(\alpha\) and \(\beta\) be the distinct roots of \(\ ax^2+bx+c=0\) then \[\Huge \lim_{x \rightarrow \alpha} \frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}=?\]
  • DLS
Attempt: \[\Large \frac{1-cosa(x-\alpha)(x-\beta)}{(x-\alpha)^2}\]

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Other answers:

  • DLS
\[\lim_{x \rightarrow \alpha}\Large \frac{1-cosa(x-\beta)}{(x-\alpha)}\]
1-cos(2x)=2 sin^2 x laga.. quadratic ko khol mat.
  • DLS
without opening the quadratic it wont solve :/ (x-alpha)^2 wont cancel i guess
do it.. sin^2 something aayega.. (x-alpha)^2 hai.. so [ sin(something)/(x-alpha)] ^2 ho jayega..
  • DLS
\[\Large \frac{ 2\sin^{2} (ax^2+bx+c)}{(x-\alpha)^2}\] this?
  • DLS
sorry upon 2 too
  • DLS
\[\Large \frac{ 2\sin^{2} \frac{ (ax^2+bx+c)}{2}}{(x-\alpha)^2}\]
yup. ab quadratic ko (x-alpha)(x-beta) likh.. multiply divide by (x-beta)^2 ka whole square.. [sin(x-alpha)(x-beta)/(x-alpha)(x-beta)]^2 *2(x-beta)^2.. pehli term sinx/x ke form me hai to 1.. bach gya 2(x-beta)^2.. to aa gya. 2*(alpha-beta)^2 ??
  • DLS
answer to galat hai khair :P
pata nhi..
  • DLS
\[(a)0\] \[(b) \frac{1}{2}a^(\alpha-\beta)^2\] \[(c) \frac{1}{2}^(\alpha-\beta)^2\] \[(d) \frac{-1}{2}a^2(\alpha-\beta)^2\]
ohho.. ax^2 + bx + c/2 tha.. :/
C hai?
  • DLS
nah :P
pta nhi.. aapko kya lgta hai?
  • DLS
x-beta wala step (2nd step) samaj nhi aya
(x-beta)^2 se multiply divide kr diya..
  • DLS
kyunkiya?
taaki sinx/x vali form ban sake.. [sin(x-alpha)(x-beta)/2]^2 hai.. to niche [(x-alpha)(x-beta)/2]^2 chahiye.. to (x-beta)^2/4 se multiply krenge..
  • DLS
bus ab rukja :P
  • DLS
@yrelhan4 (x-alpha) nahi use kar sakte (x-beta) ki jagah?
kaise? sin me x-alpha aur x- beta dono hain na.. to dono lane pdenge denominator me..
  • DLS
OH :O ab bus rukja :P
  • DLS
yo aagaya im the winner :P B hai
  • DLS
\[\LARGE \frac{2(\sin \frac{(a(x-\alpha)(x-\beta)}{2})^2}{(x-\alpha)^2} \times \frac{(\frac{a}{2})^2 \times (x-\beta)^2}{ (\frac{a}{2})^2 \times (x-\beta)^2}\]
  • DLS
u forgot about a :P
ah.. samajh gya. :/
  • DLS
:D
hmm iit. hmm
  • DLS
:P
  • DLS
1 ghanta ek question me lag raha hai :| ye 5minute ka tha,shubham ko ek minute me strike kar jata :|
ok bye.
  • DLS
thanks for the help :)
haha. :')

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