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A function f: RvecR is defined as f(x)=(...

A function `f: RvecR` is defined as `f(x)=(lim)_(nvecoo)(a x^2+b x+c+e^(n x))/(1+cdote^(n x))` is continuous on then Point lies on the space Point represents the 2-dimensional Cartesian plane Locus of point `(a ,c)a n d(c ,b)` intersect at one point Point `(a ,b ,c)` lies on the plane in space

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Discuss the continuity of 'f' in [0, 2], where f(x) = {{:(|4x - 5|[x],...

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  2. If f(x0=x+{-x}+[x],\ w h e r e\ [x] is the integral part& {x} is th...

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  3. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

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  4. Let f(x)=lim(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is con...

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  5. f(x)=(sinx+cosx)^(c o s e c x) ,-pi/2ltxlt0 a,x=0 (e^(1/x)+e^(2/x)+e...

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  6. Let sum(r=1)^nsin^(- 1)alphar=(npi)/2 for any n in N and p=prod(r=1)...

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  7. If the function f(x) =(tan(tanx)-sin(sinx))/(tanx-sinx) (x !=0): is c...

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  8. Find the following function is differentiable at a given point or n...

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  9. At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt o...

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  10. The function f(x)={{:(|x-3|",", x ge1),(((x^(2))/(4))-((3x)/(2))+(13)/...

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  11. Find the left and right hand derivative of the following function a...

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  12. Find the following function is differentiable at a given point or no...

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  13. Discuss the continuity & differentiability of the function f(x) = sin ...

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  14. Examine the continuity and differentiability of the function f(x...

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  15. If the function f(x) defined as f(x)= -x^2/x, x<=0 and f(x)=x^nsin(1/x...

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  16. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

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  17. Let f(0)=0 and f'(0)=1. For a positive integral k show that lim(x->o) ...

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  18. Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0, test the continuity & ...

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  19. If f(x)= ax^2-b, |x|<1 and f(x)=-1/|x|, |x|>=1 is derivable at x=1 th...

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  20. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

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