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Evaluate the limit lim(x->0) (e^(2x)+e^(...

Evaluate the limit `lim_(x->0) (e^(2x)+e^(-x)-2)/x`

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UNITED BOOK HOUSE-QUESTION PAPER 2015-EXERCISE
  1. Without expanding,show that |[9,9,12],[1,-3,-4],[1,9,12]|=0

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  2. Verify Rolle's theorem for function f(x) = 4^(sinx) in the interval [0...

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  3. Evaluate the limit lim(x->0) (e^(2x)+e^(-x)-2)/x

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

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

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  6. Evaluate the int sin sqrtxdx

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

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

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

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

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

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

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

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

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

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

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

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

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

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