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Evaluate:lim(x to 0)((a^x-b^x)/x)...

Evaluate:`lim_(x to 0)((a^x-b^x)/x)`

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UNITED BOOK HOUSE-SET 1-EXERCISE
  1. Prove that |[y+z,z,y],[z,z+x,x],[y,x,x+y]| =4xyz

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  2. If A=[[2,5],[1,3]] and AB = [[-13,8],[-8,5]] find B.

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  3. Evaluate:lim(x to 0)((a^x-b^x)/x)

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  4. If x= t log t,y = (log t)/t, find (dy)/(dx) when t=1

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

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  6. Solve: (dy)/(dx) = 1-x+y-xy

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  7. Show that the function f(x) = 2/3 x^3-6x^2+20x-5 has neither a maximum...

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  8. The radius of a circular plante increased at the rate of 0.002 cm/s. H...

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  9. Find the acute angle between z-axis and the straight line joining the ...

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  10. Prove that the equation of the plane which passes through the point (2...

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  11. Show that the probability that exactly one of the events A and B occur...

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  12. Show that tan^(-1)(1/sqrt3tanx/2)=1/2 cos^(-1)(1+2cosx)/(2+cosx).

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  13. If A = [[1,x,-2],[2,2,4],[0,0,2]] and A^2+2I3=3A Find x, here I3 is th...

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  14. Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

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  15. Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4a...

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  16. If f(x)= tan^(-1)(x/(1+20x^2)) show that f'(x)=5/(1+25x^2)-4/(1+16x^2)...

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  17. Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(d...

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  18. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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  19. Solve: (6x+9y-7)dx= (2x+3y-6)dy

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  20. Solve: (1-x^2)(dy)/(dx)-xy=x^2, given y = 2 when x= 0.

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