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Evaluate : underset(x to e)"Lt"(logx-1)/...

Evaluate : `underset(x to e)"Lt"(logx-1)/(x-e)`

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UNITED BOOK HOUSE-SET 9-EXERCISE
  1. Prove without expanding |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^...

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  2. Find the matrix A , when A^(-1) = [[cos theta, sin theta],[-sin theta,...

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  3. Evaluate : underset(x to e)"Lt"(logx-1)/(x-e)

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  4. Examine whether Rolle's theorem is applicable to the function f(x) = c...

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  5. int((x^2+sin^2x)/(1+x^2))sec^2xdx is equals

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  6. Find the degree and order of the differetial equation 1+((d^3y)/(dx^3)...

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  7. answer any three questions: (iii) if x>0 ,y>0 and xy=25, then find the...

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  8. Find the value of tan 44^@, given tan1^@ = 0.01745.

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  9. Find the direction cosines and direction ratios of the vector 2 hati +...

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  10. The cartesian equation of a line AB is (3-x)/1=(y+2)/-2=(z-5)/4. Find ...

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  11. If P(barA uu bar B)= 5/6, P(A)= 1/2 and P(bar B)= 2/3 show that A and ...

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  12. Find the probability that in a family of 4 children there will be at l...

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  13. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  14. If A = [[3,1],[-1,2]],I= [[1,0],[0,1]] and O = [[0,0],[0,0]] show that...

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  15. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  16. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  17. Show that the following determinant is a perfect square |[1,a,a^2],[a^...

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  18. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  19. 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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  20. Evaluate: int (dx)/(1+x^3)

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