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If (a+bx)e^(y/x)=x , Prove that x^3(d^2y...

If `(a+bx)e^(y/x)=x` , Prove that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2`

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2)...

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  2. If f(1)=3,f^(prime)(1)=2,f ^(' ')(1)=4,t h e n(f^(-1))^(' ')(3)= a. 1...

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  3. If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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  4. If R=([1+((dy)/(dx))^2]^(3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be p...

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  5. 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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  6. The function f(x)=(x^3)/8-sinpix+4 in [-4,4] does not take the value a...

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  7. If f(x)={(|x|-3 when x < 1), and (|x-2|+a , when x >= 1) & g(x)={2...

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  8. The number of points of discontinuity of f(x)=[2x]^(2)-{2x}^(2) (where...

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  9. The number of points of discontinuity of g(x)=f(f(x)) where f(x) is ...

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  10. Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b...

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  11. If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is cont...

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  12. Let f(x)=(lim)(n rarr oo)sum(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (...

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  13. Let f(x)={lim(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/...

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  14. If f(x)={(sinx, x != npi " and " n in I2), (2, " x=npi):} and g(x)={(x...

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  15. The number of points at which g(x)=1/(1+2/(f(x))) is not differentiabl...

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  16. If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is a. x...

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  17. Consider two functions y=f(x) and y=g(x) defined as f(x)={[a x^2 +b...

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  18. Let f be a function with continuous second derivative and f(0)=f^(prim...

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  19. Let f(x) be a function defined on (-a ,a) with a > 0. Assume that f(x)...

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  20. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

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