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if `x<1` then `1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If Pn is the sum of a GdotPdot upto n terms (ngeq3), then prove that (...

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  2. If y=f(a^x)a n df^(prime)(sinx)=(log)e x ,then f i n d ((dy)/(dx)), if...

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  3. if x<1 then 1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo

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  4. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3))

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  5. Find ("lim")(xto2)(xf(2)-2f(x))/(x-2) if f(2)=4 and f′(2)=1

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  6. If y=x^(x^(x^x...oo) , find (dy)/(dx)

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  7. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a)(e^(sqr...

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  8. Differentiate sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))) with respect to x

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  9. If f(x)=|sinx-|cosx||, then the value of f^'(x) at x=(7pi)/6 is (a) ...

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  10. If y=(tanx)^((tanx)^((tanx).... ∞) ,then find (dy)/(dx) at x=pi/4

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  11. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x) ...

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  12. Differentiate the function with respect to x using the first principle...

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  13. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2) is (a)3/2 (b) 3/(4t) (c) 3/(2t) (...

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  14. Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...

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  15. If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) ...

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  16. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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  17. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

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  18. If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

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  19. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

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  20. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

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