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Prove that, q(x) = {(|x|/x, when x ne 0)...

Prove that, q(x) = `{(|x|/x, when x ne 0),(0, when x = 0):}` is discontinuous at x = 0.

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UNITED BOOK HOUSE-SET (11)-EXERCISE
  1. Find the real values of K for which the following system of linear equ...

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  2. If A = [[2,3], [4,5]], prove that A - A^(T) is a skew-symmetric matrix...

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  3. Prove that, q(x) = {(|x|/x, when x ne 0),(0, when x = 0):} is disconti...

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  4. State Rolle's theorem.

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  5. Evaluate: int xe^x dx

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

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  7. Show that the function f(x) = log x has neither a maximum nor a minium...

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  8. Let V and S be the volume and surfacea area of a sphere with radius re...

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  9. Find the direction cosines of the straight line which makes equal angl...

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  10. Show that the lines (x - 1)/3 = (y + 1)/2= (z - 1)/5 and (x + 2) / 4 =...

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  11. If A and B are two events such that P(A) = P(B) = 1, then show that, P...

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  12. Eight coins are thrown simultaneously. Show that the probability of ge...

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  13. If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] =...

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  14. Provet that the producet of the matrics [[cos^2 alpha cos alpha sin al...

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  15. Solve :|(x + a, b, c),(a, x+b, c),(a, b, x + c)|=0

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  16. If f(x)= ((a+x)/(b+x))^(a+b+2x) then prove that f'(0)= [2log(a/b)+(b...

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  17. If y = e^u and u = f(x), show that,(d^2y)/(dx^2)= e^u [(d^2u)/(dx^2) +...

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  18. int dx/(x^n(1+x^n)^(1/n)) is

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  19. Solve: (x^2 + y^2).dx-2xydy = 0, given y = 0 when x = 1

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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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