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Let f(x+y) = f(x) f(y) and f(x) = 1 + x ...

Let `f(x+y) = f(x) f(y) and f(x) = 1 + x g(x) G(x)` where `lim_(x->0) g(x) =a and lim_(x->o) G(x) = b. `Then `f'(x)` is

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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Discuss the continuity of the function f(x) = underset(n rarr oo)(lim)...

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  2. If a function f : [-2a, 2a] rarr R is an odd function such that f(x) =...

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  3. Let f(x+y) = f(x) f(y) and f(x) = 1 + x g(x) G(x) where lim(x->0) g(x)...

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  4. Let f(x) be a continuous defined for 1le xle 3. if f(x) takes ra...

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  5. Let f(x) = [ n + p sin x], x in (0,pi), n in Z, p is a prime number an...

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  6. f(x)=min{1,cosx,1-sinx},-pilexlepi, then

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  7. A function f(x) is defined in the interval [1,4) as follows f(x)={{:(,...

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  8. Discuss the continuity of f(x)=(lim)(n->oo)(x^(2n)-1)/(x^(2n)+1)

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  9. Discuss the continuity of function f(x)={{:(1,"if x is rational"),(...

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  10. Let f(x)={(tan^(-1)x, , |x|ge1),((x^(2)-1)/4, , |x|lt1):} then domain ...

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  11. No. of points of discontinuity of [ 2 x^3 - 5] in [1,2] is

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  12. Discuss the differentiability of f(x)=m a x{2sinx ,1-cosx}AAx in (0,...

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  13. Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):},...

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  14. Let y=tan((pi)/4+x/2). Then (dy)/(dx) at x=(pi)/4

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  15. Let f(x) = lim( n to oo) m ( sin x)^(2n) then which of the follow...

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  16. If f is a periodic function then

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  17. If f(x+y)=f(x)f(y) for all x and y and f(X)=1+g(x)G(x) where lim(xto 0...

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  18. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

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  19. (tanx)^(y)=(tany)^(x) find dy/dx

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  20. If f(x+2)=(x+3)^(2)-2x, then f(x)=

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