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(lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s...

`(lim)_(hvec0)((e+h)^(1n(e+h))-e)/hi s____`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

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  2. Let y=(2^((log)2 1/4x)-3^((log)(27) (x^2+1)^3-2x))/(7^(4(log)(49)x)-...

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  3. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

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  4. If (x-a)^2+(y-b)^2=c^2, for some c >0, prove that([1+((dy)/(dx))^2]^(...

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  5. if y=(x^2-1)^m , then the (2m)th differential coefficient of y is

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  6. If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prim...

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  7. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  8. If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)...

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  9. Let f(x)=(x-1)(x-2)(x-3)--(x-n),n in N ,a n df(n)=5040. Then the valu...

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  10. If y=((a x+b))/((x^2+c)) , then find dy/dx .

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  11. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  12. y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)),...

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  13. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 ...

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  14. Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

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  15. If e^y(x+1)=1, show that (d^2y)/(dx^2)=((dy)/(dx))^2

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  16. If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((...

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  17. If y=cos^(-1)(cosx),then (dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-...

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  18. If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x=(5pi)/4 is equal to (a) 1 (b...

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  19. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a...

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  20. If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt...

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