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Answer all questions (j) A function f(...

Answer all questions
(j) A function `f(x)` is defined as `f(x) = {{:((x^2 - x - 6)/( x-3)",","if" xne 3),(5",","if"x=3):}` Show that `f(x)` is continuous at `x=3`.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION C (30 MARKS)
  1. Answer all questions (j) A function f(x) is defined as f(x) = {{:((x...

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  2. If x = sin^(-1) ((2t)/( 1 + t^(2) )) and y= tan^(-1) ((2t)/( 1-t^(2) )...

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  3. Find the equations of the tangent to the curve y = x^(2) - 2x + 7, whi...

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  4. Find the area of the region bounded by y=-1, y=2, x=y^(3) and x =0.

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  5. Solve (dy)/(dx) = e^(x +y) + e^(-x +y).

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  6. Evaluate int e^(x) ((1 + sin x cos x)/( cos^(2) x)) dx.

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  7. Find the points on the line (x+2)/(3) = (y+1)/(2) = (z-3)/(2)  at a d...

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  8. Prove that cos^(-1)[(cos alpha +cos beta)/(1+cos alpha cos beta)]=2tan...

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  9. Answer any one question (b) A factory makes tennis rackets and crick...

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  10. Let f : N rarr N be defined by f(n) = {{:((n+1)/(2), if "n is odd"),...

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  11. Answer any one question (a) Determine the product [{:(-4,4,4),(7,1,3...

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  12. Three cards are drawn successively, without replacement from a pack of...

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  13. Find the inverse of the following matrix using elementary transformati...

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  14. If x = sin^(-1) ((2t)/( 1 + t^(2) )) and y= tan^(-1) ((2t)/( 1-t^(2) )...

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  15. Find the equations of the tangent to the curve y = x^(2) - 2x + 7, whi...

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  16. Find the area of the region bounded by y=-1, y=2, x=y^(3) and x =0.

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  17. Solve (dy)/(dx) = e^(x +y) + e^(-x +y).

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  18. Evaluate int e^(x) ((1 + sin x cos x)/( cos^(2) x)) dx.

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  19. Find the points on the line (x+2)/(3) = (y+1)/(2) = (z-3)/(2)  at a d...

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  20. A variable plane is at a constant distance 3r from the origin and meet...

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  21. Prove that cos^(-1)[(cos alpha +cos beta)/(1+cos alpha cos beta)]=2tan...

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