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Given a real-valued function `f` such that `f(x)={(tan^2{x})/((x^2-[x]^2) sqrt({x}cot{x}),for x<0,fx >0` Where `[x]` is the integral part and `{x}` is the fractional part of `x ,` then `("lim")_(xvec0^+)f(x)=1` , `("lim")_(xvec0^-)f(x)=cot1`, `cot^(-1)(("lim")_(xvec0^-)f(x))^2=1`, `tan^(-1)(("lim")_(xvec0^+)f(x))=pi/4`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is...

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  2. Evaluate underset(xtooo)lim(sqrt(25x^(2)-3x)+5x).

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  3. Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

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  4. Evaluate underset(xtooo)lim((x^(2)+x-1)/(3x^(2)+2x+4))^((3x^(2)+x)/(x-...

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  5. L=lim(x to a)(|2sinx-1|)/(2sinx-1)dotT h e n (a) limit does not exis...

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  6. If [x] denotes the greatest integer less than or equal to x, then eval...

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  7. f(x)=("lim")(n-&gt;oo)x/(x^(2n)+1)dotT h e n , A. f(1^+)+f(1^(-1))...

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  8. Evaluate the limit: lim(x->1)((2x-3)(sqrt(x)-1))/(2x^2)

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

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

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  11. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

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  12. lim(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ) is ...

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  13. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

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  14. If underset(ntooo)lim(n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then ...

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  15. If ("lim")(xveca)[f(x)g(x)] exists, then both ("lim")(xveca)f(x)a n d(...

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  16. If f(x)=underset(ntooo)limn(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) i...

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  17. lim(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

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  18. underset(xto1)lim[cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the...

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  19. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

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  20. Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not gr...

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