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("lim")(xvecoo)[(x^4sin(1/x)+x)/((1+|x|^...

`("lim")_(xvecoo)[(x^4sin(1/x)+x)/((1+|x|^3)]=______`

A

1

B

-1

C

0

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,
`lim_(xto oo) {(x^4sin((1)/(x))+x^2)/(1+|x^3|)}`
` =lim_(yto oo)(y^4sin((-1)/(y))+y^2)/(1+|x|^3),"where "y=-x`
` =lim_(yto oo) (-y^4sin((1)/(y))+y^2)/(1+y^3)`
` lim_(yto oo) (-ysin((1)/(y))+(1)/(y))/((1)/y^(3)+1)=(-1+0)/(0+1)=-1`
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
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  2. If [.] denotes the greatest intger function, then lim(xrarr0) (tan([-2...

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  3. ("lim")(xvecoo)[(x^4sin(1/x)+x)/((1+|x|^3)]=

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  4. lim(n to oo) (1+x)(1+x^(2))(1+x^(4))……………(1+x^(2n)),|x|lt1 is

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  5. If phi(x)=lim(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the f...

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  6. The value of lim(x to pi//2){1^(sec^2x) +2^(sec^2x) +3^(sec^2x)+.......

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  7. If l =lim(xrarr0) (tanx^(n))/((tanx)^m), where m,n in N, then

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  8. If lim(x->oo)((1+a^3)+8e^(1/ x))/(1+(1-b^3)e^(1/ x))=2, then there exi...

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  9. lim(xrarr-1)((x^4+x^2+x+1)/(x^2-x+1))^((1-cos(x+1))/((x+1)^2)) is equa...

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  10. lim(xrarre) (log(e)x-1)/(|x-e|) is

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  11. The value of underset(ntooo)lim[(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...

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  12. If the graph of the function y=f(x) has a unique tangent at the point ...

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  13. Let f(x)=3x^10-7x^8+5x^6-21x^3+3x^2-7 , then the value of lim(h->0)...

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  14. Let a=min{x^(2)+2x+3,x epsilonR} and b=lim(x theta to 0)(1-cos theta)/...

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  15. lim(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((2n+1)(2n+3)) is equal to

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  16. If lim (x to 0) ((sin (sin x)-sin x))/(ax ^(3) + bx ^(5) +c)=-(1)/(12)...

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  18. lim(x->alpha)(tanxcotalpha)^(1/(x-alpha)) is equal to

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  19. lim(xtoa){[((a^(1//2)+x^(1//2)),(a^(1//4)-x^(1//4)))^(-1)-(2(ax)^(1//4...

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  20. The value of lim(nto oo){3sqrt(n^2-n^3)+n}, is

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