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If sin^(-1) ((x^2-y^2)/(x^2+y^2))=k, k i...

If `sin^(-1) ((x^2-y^2)/(x^2+y^2))=k`, k is a constant, then prove that `(dy)/(dx)=y/x` .

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UNITED BOOK HOUSE-QUESTION PAPER 2015-EXERCISE
  1. Evaluate the limit lim(x->0) (e^(2x)+e^(-x)-2)/x

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  2. If the function f(x) = {((sin x)/(kx)+k, x!=0),(2,x=0):} is continuous...

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  3. If sin^(-1) ((x^2-y^2)/(x^2+y^2))=k, k is a constant, then prove that ...

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  4. Evaluate the int sin sqrtxdx

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  5. Find the differential equation of the curves given by y = Ae^(2x)+Be^(...

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  6. Find the vector equation of the line whose Cartesian equation is given...

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  7. If veca and vecb are two vectors such that |veca|=2,|vecb|=3 and veca....

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  8. Find out the mean and variance of the following probability distributi...

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  9. Find the probability that birthdays of any two members out of five me...

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  10. Prove that tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x.

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  11. If A = ([1,4],[2,3]) then show that A^2-4A-5I = theta and using this f...

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  12. Solve the following equations by Cramer's method: x+y=1,y+z= 2,x+z=3.

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  13. Show that |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3.

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  14. Solve for x: |[x,c+x,b+x],[c+x,x,a+x],[b+x,a+x,x]|=0

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  15. Find (dy)/(dx) where x= cos^(-1)(8t^4-8t^2+1) y =sin^(-1)(3t-4t)^3...

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  16. Evaluate: int(2^xdx)/sqrt(4^x-2^(x+2)+5)

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  17. Evaluate : int (3x+5)/(x^3-x^2-x+1)dx

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  18. SolveL (1+y)^2dx=(tan^(-1)y-x)dy, given that y= 0 when x= -1.

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  19. If the rate of increase of population is 5% per year, then in how man...

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  20. Find vecc, when vecaxxvecc=vecb and veca.vecc= 3 where veca= hatr+hatj...

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