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If y=log(1/x) , show that dy/dx+e^y=0...

If `y=log(1/x)` , show that `dy/dx+e^y=0`

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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. Find dy/dx of the following x=a(t-sint) , y=a(1-cost)

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  2. Find dy/dx of the following y=e^tcost , x=e^tsint

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  3. If y=log(1/x) , show that dy/dx+e^y=0

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  4. If e^y(x+1)=1 . Show that dy/dx=-e^y

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  5. If e^y(x+1)=1 . Show that (d^2y)/dx^2=(dy/dx)^2

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  6. Evalute lim(xrarr0)frac(kcosx)(pi-2x) (Hint: Put pi-2x=y , where k i...

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  7. Find the value of k if f(x) is a continious function give by f(x)={(...

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  8. If f(x)={(x-absx,x<2),(0,x=2),(3x-5,x>2):} Find lim(xrarr2)f(x)

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  9. Is f(x) =x^2continuous at x=2 ?

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  10. If x=2costheta , y=3sintheta Find dy/dx .

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  11. If x=2costheta , y=3sintheta Find (d^2y)/(dx^2) .

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  12. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  13. Find dy/dx If y=sin^(-1)(frac(1-x^2)(1+x^2)) , 0 < x < 1

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  14. Let f(x)={(cosx,0lexlec),(sinx,c<xlepi)} Find the value of c if f is...

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  15. Find dy/dx if x=2sintheta , y=3costheta

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  16. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

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  17. If x=a^(sin^(-1)t) , y=a^(cos^(-1)t) , a>0 , show that dy/dx=-y/x

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  18. If f(x)={(1-x,0<x<1),{(1+x,1<x<2):} then which of the following is not...

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  19. If (1, xle 3), (ax+b, 3<x<5),(7,5lex) find f(3^+) and f(3^-)

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  20. If {(1,xle3), (ax+b,3<x<5) ,(7,5lex):} hence find the value of 'a' a...

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