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If f(x+y)=f(x)+f(y),AAx ,\ y in R then ...

If `f(x+y)=f(x)+f(y),AAx ,\ y in R` then prove that `f(k x)=kf(x)for\ AAk ,\ x in Rdot`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Suppose f is a derivable function that satisfies the equation f(x+y...

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  2. If f(x+y)=f(x)dotf(y),\ AAx in R\ a n df(x) is a differentiability...

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  3. If f(x+y)=f(x)+f(y),AAx ,\ y in R then prove that f(k x)=kf(x)for\ AA...

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  4. Discuss the differentiability of f(x)={(sinx^2)/x ,x!=0 0,x=0a tx=0

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  5. Discuss the differentiability of f(x)=|x|||x-1|dot

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  6. Discuss the differentiability of f(x)=m a xi mu m{2sinx ,1-cosx}AAx...

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  7. Discuss the differentiability of f(x)=e^(-|x|)

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  8. If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b...

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  9. Find the values of aa n db if f(x)={a+sin^(-1)(x+b),xgeq1x ,x<1 is di...

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  10. Discuss the continuity and differentiability of f(x)=|x+1|+|x|+|x-1|AA...

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  11. Find x where f(x)=m a xi mu m{sqrt(x(2-x)),2-x} is non-differentiable.

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  12. Discuss the differentiability of f(x)=|px[x]| ,-1 < x <= 2

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  13. Discuss the differentiability of f(x)="max"{tan^(-1)x ,cot^(-1)x}dot

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  14. Find the values of aa n db if f(x)={a x^2+1,xlt=1 ,x^2+a x+b ,x &gt...

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  15. Discuss the differentiability of f(x=cos^(-1)((1-x^2)/(1+x^2))

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  16. The value of (lim)(x->0)(sqrt(2)-sqrt(1+cos x))/(sin^2x) is 1/(2sqrt(...

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  17. If a1=1\ a n d\ a(n+1)=(4+3an)/(3+2an),\ ngeq1\ a n d\ if\ (lim)(n->oo...

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  18. Evaluate the limit: ("lim")(nvecoo)cos(pisqrt(n^2+n))w h e nni sa nin ...

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  19. lim(n->oo)prod(r=3)^n(r^3-8)/(r^3+8)

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

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