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underset(xto0)lim[(sin(sgn(x)))/((sgn(x)...

`underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))],` where `[.]` denotes the greatest integer function, is equal to

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

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

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  3. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

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  4. underset(xtooo)lim(2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

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  5. If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")(xrarrpi/2)f(x)=-oo (b...

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  6. lim(x->-oo)(x^2*tan(1/x))/(sqrt(8x^2+7x+1)) is

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  7. T1 is an isosceles triangle in circle C. Let T2 be another ísoscele...

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  8. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  9. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is :

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  10. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e ...

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  11. lim(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 ...

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  12. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  13. "Find"(dy)/(dx)"if "y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  14. (c)answer any three questions: 1. if y=sin ^(-1) ((2x)/(1+x^2)) , find...

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  15. If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then f...

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  16. Find (dy)/(dx) for the functions: y=(x+sinx)/(x+cosx)

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  17. Find the derivative of the function given by f(x)=(1+x)(1+x^2)(1+x^4)(...

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  18. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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  19. Let f(x)=xsinpix ,\ x >0 . Then for all natural numbers n ,\ f^(pr...

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  20. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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