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If x = a ( t+ sin t) and y = a (1- cos t...

If x = a `( t+ sin t) and y = a (1- cos t) " find " (dy)/(dx)`

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`(dx)/(dy) = a(1+cos t) = - a sin t = 2a cos^(2) . t/2 , (dy)/(dt) - a sin . t/a cos . t/2 `
`(dy)/(dx) =((dy)/(dx))/((dx)/(dt))=(2a sin . t/2 cos . t/2)/(2a.cos^(2). t/2)=(sin. t/2)/(cos. t/2) = tan . t/2 `
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ICSE-VECTORS SCALARS ELEMENTARY CALCULUS -EXAMPLES
  1. Differentiate w.r.t x, y y = (4x^(2) - 5x + 10)^(10)

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  2. Differentiate w.r.t x , y = x^(sinx)

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  3. Differentiate w.r.t x Given x =a cos^(3) theta , y = b sin^(3) theta

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  4. Integrate the following 3x^(2)- 6x +1/(x^(3))

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  5. Integrate the following cos^(2) 3x

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  6. Integrate the following sin^(3) x cos^(4) x

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  7. Integrate the following 1/(sqrt(x^(2)+a^(2)))

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  8. Integrate the following x log x

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  9. Differentiate the following with respect to x 2x^(3)- 9 - 3x^(2)

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  10. Differentiate the following with respect to x 2 sin x - 3 log x

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  11. Differentiate the following with respect to x (3x^(2) - 5) (x^(2)+7...

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  12. Differentiate the following with respect to x x^(2)e^(x) sin x

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  13. Differentiate the following with respect to x e^(x)//(1 + sin x)

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  14. Differentiate the following with respect to x x^(2) -1//x^(2)+1

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  15. Differentiate the following with respect to x sin^(-1)sqrt(x)

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  16. Differentiate the following with respect to x cos^(-1) sqrt((1+cosx...

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  17. Differentiate the following with respect to x x^(sin x)

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  18. If x = a ( t+ sin t) and y = a (1- cos t) " find " (dy)/(dx)

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  19. Differentiate w.r.t x Given x =a cos^(3) theta , y = b sin^(3) theta

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  20. Given that y = 3 cos x + 2 sin x . Show that (d^(2)y)/(dx^(2)) + y...

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