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Evaluate a,b,c and d if lim(xto oo)(sq...

Evaluate `a,b,c` and d if
`lim_(xto oo)(sqrt(x^(4)+ax^(3)+3x^(2)+bx+2)-sqrt(x^(4)+2x^(3)-cx^(2)+3x-d))=4`

A

3

B

5

C

2

D

any real number

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`lim_(xto oo) (sqrt(x^4+ax^3+3x^2+bx+2)-sqrt(x^4+2x^3-cx^2+3x-d))`
`lim_(xto oo) ((x^4+ax^3+3x^2+bx+2)-(x^4+2x^3-cx^2+3x-d))/ (sqrt(x^4+ax^3+3x^2+bx+2)+sqrt(x^4+2x^3-cx^2+3x-d))`
`lim_(xto oo) ((a-2)x^3+(3+c)x^(2)+(b-3)x+(2+d))/ (sqrt(x^4+ax^3+3x^2+bx+2)+sqrt(x^4+2x^3-cx^2+3x-d))`
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
  1. lim(nrarr oo) (a^nb^n)/(a^n+b^n), where 1lt b lt a , is equal to

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  2. lim(xrarr oo) (4^(1//n)-1)/(3^(1//n)-1) is equal to

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  3. Evaluate a,b,c and d if lim(xto oo)(sqrt(x^(4)+ax^(3)+3x^(2)+bx+2)-s...

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  4. if lim(x->0)(1+a x)^(b / x)=e^2, where a and b are natural numbers, th...

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  5. lim(nto oo) (2^n+5^n)^(1//n) is equal to

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  6. lim(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer le...

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  7. lim(xrarr oo) (logx)/([x]) , where [.] denotes the greatest integer fu...

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  8. lim(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the grea...

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  9. If a .lim(xrarr 1) x^(1//1-x)+b=e^(-1)(a ge 1,bge 0) , then

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  10. lim(xrarr -1) (cos 2 -cos 2x)/(x^2-|x|) is equaol to

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  11. Lim(x->oo) ((x/(x+1))^a + sin (1/x))^x is equal to

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  12. If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...

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  13. If {x} denotes the fractional part of x, then lim(xrarr1) (x sin {x})/...

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  14. lim(xrarr0+) (sinsqrt(x))/(sqrt(sinx)) is equal to

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  15. If alpha and beta are roots of the equation ax^2+bx +c=0, then lim(xr...

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  16. If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim(xto...

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  17. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

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  18. If F(x) = {(sin{cosx})/(x-pi/2),x!=pi/2 and 1,x=pi/2, where {.} repres...

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  19. The value of lim(xrarr oo) 1+(1)/(x^n)^x,ngt 0, is

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  20. lim(x->a^-) {(|x|^3)/a-[x/a]^3} ,(a > 0), where [x] denotes the greate...

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