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lim(xto0^(+)) (sum(r=1)^(2n+1)[x^(r)]+(n...

`lim_(xto0^(+)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x),` where `ninN` and `[.]` denotes the greatest integer function, equals

A

0

B

1

C

-1

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto0^(-))lim(sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x)=underset(xto0^(-))lim(sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(x)`
`=underset(xto0^(-))lim([x]+[x^(2)]+[x^(3)]+...+[x^(2n+1)]+(n+1))/(x)`
`=underset(xto0^(-))lim(ubrace((-1)+(-1)+...+(-1))_((n+1)"times")+(n+1))/(x)=underset(xto0^(-))lim(0)/(x)=0`
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CENGAGE-LIMITS-Exercise (Single)
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  2. If x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xvecoo)xn is -1 ...

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  3. lim(xto0^(+)) (sum(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where nin...

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  4. lim(xtooo) (sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1)is equal to

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  6. The value of lim(xto pi) (1+cos^(3)x)/(sin^(2)x)" is "

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  7. The value of ("lim")(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a)1/(...

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  8. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  9. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  10. about to only mathematics

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  11. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

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  12. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

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  13. evaluate (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underse...

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  14. lim(x to oo )((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2)) is equal to

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  15. ("lim")(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n-1))i se q u a lto 0 (b) 2...

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  16. ("lim")(xvecoo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45))i se q u a lto 16 (...

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  17. lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

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  18. about to only mathematics

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  19. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

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  20. ("lim")(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(x)+...+nsqrt(n))/(sqrt((2x-3))...

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