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Suppose f is a derivable function tha...

Suppose `f` is a derivable function that satisfies the equation `f(x+y)=f(x)+f(y)+x^2y+x y^2` for all real numbers `x\ a n d\ y` . Suppose that `(lim)_(x->0)(f(x))/x=1,\ fin d` `f(0)` b. `f^(prime)(0)` c. `f^(prime)(x)` d. `f(3)`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) f...

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  3. Suppose f is a derivable function that satisfies the equation f(x+y...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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