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Let alpha and beta be the distinct roots...

Let `alpha` and `beta` be the distinct roots of `ax^(2) + bx + c = 0`. Then `underset(x to alpha)(lim) (1 - cos (ax^(2) + bx + c))/((x - alpha)^(2))` equal to

A

0

B

`(1)/(2)(alpha-beta)^2`

C

`(a^2)/(2)(alpha-beta)^2`

D

`-(a^2)/(2)(alpha-beta)^2`

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
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  2. If [x] denotes the greatest integer less than or equal to x,then the v...

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  3. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0. Then ...

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  4. If f(x)={(xsin,((1)/(x)),xne0),(0,,x=0):} Then, lim(xrarr0) f(x)

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  5. lim(xto-pi)(|x+pi|)/(sin x) is

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  6. If lim(x->oo) (sqrt(x^2-x+1)-ax-b)=0 then the value of a and b are giv...

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  7. lim(xto1) (sum(r=1)^(n)x^(r)-n)/(x-1) is equal to

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  8. lim(x->pi/4)(2sqrt(2)-(cosx+sinx)^3)/(1-sin2x)=

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  9. The value of lim(n->oo)(1.sum(r=1)^n(r)+2.sum(r=1)^(n-1)(r)+3sum(r=1)^...

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  10. The value of lim(xtooo) {(1)/(3)+(2)/(21)+(3)/(91)+...+(n)/(n^4+n^2+1...

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  11. The value lim(xrarr pi//2)(sinx)^(tanx), is

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  12. The value of lim(xrarroo) (5^(x+1)-7^(x+1))/(5^x-7^x),is

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  13. The value of lim(xrarr3)(3^x-x^3)/(x^x-3^3), is

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  14. lim(n->oo)[log(n-1)(n)logn(n+1)*log(n+1)(n+2).....log(n^k-1) (n^k)] i...

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  15. The value of underset(mtooo)lim("cos"(x)/(m))^(m) is

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  16. The value of lim(xrarroo)(sqrt(n^2+1)+sqrt(n))/((n^4+n)^(1/4)+4sqrt(n)...

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  17. The value of lim(xrarr0) (x^2sin((1)/(x)))/(sinx), is

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  18. If l=lim(xto-2) (tanpix)/(x+2)+lim(xtooo) ( (1+1)/(x^2)^2), then which...

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  19. The value of lim(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] ...

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  20. lim(xto oo) (1^2.n+2^2.(n-1)+3^2.(n-2)+......+n^2.1)/(1^3+2^3......+n^...

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