## DLS 2 years ago limits(38)

1. hba

lol wut?

2. DLS

Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$\ ax^2+bx+c=0$$ then $\Huge \lim_{x \rightarrow \alpha} \frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}=?$

3. DLS

Attempt: $\Large \frac{1-cosa(x-\alpha)(x-\beta)}{(x-\alpha)^2}$

4. DLS

$\lim_{x \rightarrow \alpha}\Large \frac{1-cosa(x-\beta)}{(x-\alpha)}$

5. yrelhan4

1-cos(2x)=2 sin^2 x laga.. quadratic ko khol mat.

6. DLS

without opening the quadratic it wont solve :/ (x-alpha)^2 wont cancel i guess

7. yrelhan4

do it.. sin^2 something aayega.. (x-alpha)^2 hai.. so [ sin(something)/(x-alpha)] ^2 ho jayega..

8. DLS

$\Large \frac{ 2\sin^{2} (ax^2+bx+c)}{(x-\alpha)^2}$ this?

9. DLS

sorry upon 2 too

10. DLS

$\Large \frac{ 2\sin^{2} \frac{ (ax^2+bx+c)}{2}}{(x-\alpha)^2}$

11. yrelhan4

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 ??

12. DLS

answer to galat hai khair :P

13. yrelhan4

pata nhi..

14. DLS

$(a)0$ $(b) \frac{1}{2}a^(\alpha-\beta)^2$ $(c) \frac{1}{2}^(\alpha-\beta)^2$ $(d) \frac{-1}{2}a^2(\alpha-\beta)^2$

15. yrelhan4

ohho.. ax^2 + bx + c/2 tha.. :/

16. yrelhan4

C hai?

17. DLS

nah :P

18. yrelhan4

pta nhi.. aapko kya lgta hai?

19. DLS

x-beta wala step (2nd step) samaj nhi aya

20. yrelhan4

(x-beta)^2 se multiply divide kr diya..

21. DLS

kyunkiya?

22. yrelhan4

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..

23. DLS

bus ab rukja :P

24. DLS

@yrelhan4 (x-alpha) nahi use kar sakte (x-beta) ki jagah?

25. yrelhan4

kaise? sin me x-alpha aur x- beta dono hain na.. to dono lane pdenge denominator me..

26. DLS

OH :O ab bus rukja :P

27. DLS

yo aagaya im the winner :P B hai

28. DLS

$\LARGE \frac{2(\sin \frac{(a(x-\alpha)(x-\beta)}{2})^2}{(x-\alpha)^2} \times \frac{(\frac{a}{2})^2 \times (x-\beta)^2}{ (\frac{a}{2})^2 \times (x-\beta)^2}$

29. DLS

30. yrelhan4

ah.. samajh gya. :/

31. DLS

:D

32. yrelhan4

hmm iit. hmm

33. DLS

:P

34. DLS

1 ghanta ek question me lag raha hai :| ye 5minute ka tha,shubham ko ek minute me strike kar jata :|

35. yrelhan4

ok bye.

36. DLS

thanks for the help :)

37. yrelhan4

haha. :')