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lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/(...

`lim_(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1))` is equal to

A

-1

B

1

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1))`
`(x^(4)(1-tan^(2)x+tan^(4)x))/(tan^(4)x(tan^(4)x-tan^(2)x+1))=(x^(4))/(tan^(4)x),xne0`
`:." "underset(xto0)lim(x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1))=underset(xto0)lim(x^(4))/(tan^(4x))=1`
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  2. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)), where a , b , c in R ~{0},exis...

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

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  4. ("lim")(xvec1)(1-x^2)/(s in2pix)i se q u a lto 1/(2pi) (b) -1/pi (c...

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

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  6. ("lim")(xvec0)((x+y)sec(x+y)-xsecx)/yi se q u a lto (a)secx(xtanx+1)...

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  7. lim(xto0)(1+x)^(1/(3x))

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  8. ("lim")(n->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

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  9. 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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  10. ("lim")(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to ...

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

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

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  13. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

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

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

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  16. The value of ("lim")(xvec1^-)(1-sqrt(x))/((ccos^(-1)x)^2) is 4 (b) ...

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  17. ("lim")(xvecpi/2)(sin(xcosx)/("cos"(xsinx)i se q u a lto 0 (b) p/2 (...

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  18. ("lim")(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the ...

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  19. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  20. If f(x)=lim(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to ...

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