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Let lim(x->0)([x]^2)/(x^2)=l and lim(...

Let `lim_(x->0)([x]^2)/(x^2)=l and lim_(x->0)([x^2])/(x^2)=m ,` where `[dot]` denotes greatest integer. Then (a)`l` exists but `m` does not (b)`m` exists but `l` does not (c)both l and m exist (d) neither `lnorm` exists

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. The value of ("lim")(xto1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(si...

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  2. The value of lim(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (w...

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  3. Let lim(x-&gt;0)([x]^2)/(x^2)=l and lim(x-&gt;0)([x^2])/(x^2)=m , whe...

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  4. ("lim")(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest ...

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  5. ("lim")(x->0)[(sin(sgn(x)))/((sgn(x)))], where[dot] denotes the greate...

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  6. lim(x->0) (2+2x+sin2x)/((2x+sin2x)e^sinx) is

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

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

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

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  10. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  11. ("lim")(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s e^((1-e)) (b) e^(((1-e)...

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

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  13. ("lim")(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) ...

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

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  15. "F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  16. If y=sin^(-1)((2x)/(1+x^2)), then find (dy)/(dx)

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

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

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

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

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