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lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^...

`lim_(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1))` is equal to

A

4

B

`(1//2`

C

2

D

`1//4`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xtooo)lim(x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1))=underset(xtooo)lim(x^(2)"tan"(1)/(x) )/(-xsqrt(8+(7)/(x)+(1)/(x^(2))))`
`=underset(xtooo)lim("tan"(1)/(x) )/((1)/(x)sqrt(8+(7)/(x)+(1)/(x^(2))))=-(1)/(2sqrt(2))`
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CENGAGE-LIMITS-Exercise (Single)
  1. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  2. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  3. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  4. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  5. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  6. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  7. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  8. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  9. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  10. lim(ntooo) sum(x=1)^(20)cos^(2n)(x-10) is equal to

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  11. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  12. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  13. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  14. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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  15. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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  16. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  17. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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  18. The value of lim(xto1^(-)) (1-sqrt(x))/((cos^(-1)x)^(2)) is

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  19. lim(xto pi//2) (sin(xcosx))/(cos(xsinx)) is equal to

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  20. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

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