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Math Help - Caclulas practise paper

  1. #1
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    Caclulas practise paper

    Hello. Need some awnsers to mark my practise exam papper. Please and thank you.

    1. Differentiate each of the following with respect to x
    a. 2x2-4x+3/x2
    b. (4x3-2x2-1)5
    c. (sin 4x) (e3x)
    d. x+2/3x-1

    2. if f(x) = e5x find f(x)

    3. if x and y are defined parametrically as x=cos (θ) and y = cosec (θ), find dy/dx

    4. Find the point of inflection of the function described by f(x) x36x2+12x - 4
    Apply an appropriate test to make sure it is a point of inflection you found.

    5. The cost, $C of running a dinghy with a small out board engine is C = 8/v2 + v/27, where v(km/hr) is the constant speed for the journey.
    At what speed (to 2 d.p.) should the dinghy be run for the most economical trip?
    Find the cost.
    Apply an appropriate test to make sure it is a minimum cost you found.

    6. A curve is defined by the parametric equations x= 4t and y=t2-4
    Find the equation of the tangent at the point where t=2

    7. a large cube of ice is melting so that its volume, v, is decreasing at the rate of 60 cm3/s.
    Find the rate at which each side, x, of the cube is decreasing at the moment when the length of each side is 20cm.

    Thanks alot.
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  2. #2
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    Quote Originally Posted by balliztiks View Post
    Hello. Need some awnsers to mark my practise exam papper. Please and thank you.

    1. Differentiate each of the following with respect to x
    a. 2x2-4x+3/x2
    b. (4x3-2x2-1)5
    c. (sin 4x) (e3x)
    d. x+2/3x-1

    2. if f(x) = e5x find f(x)

    3. if x and y are defined parametrically as x=cos (θ) and y = cosec (θ), find dy/dx

    4. Find the point of inflection of the function described by f(x) x36x2+12x - 4
    Apply an appropriate test to make sure it is a point of inflection you found.

    5. The cost, $C of running a dinghy with a small out board engine is C = 8/v2 + v/27, where v(km/hr) is the constant speed for the journey.
    At what speed (to 2 d.p.) should the dinghy be run for the most economical trip?
    Find the cost.
    Apply an appropriate test to make sure it is a minimum cost you found.

    6. A curve is defined by the parametric equations x= 4t and y=t2-4
    Find the equation of the tangent at the point where t=2

    7. a large cube of ice is melting so that its volume, v, is decreasing at the rate of 60 cm3/s.
    Find the rate at which each side, x, of the cube is decreasing at the moment when the length of each side is 20cm.

    Thanks alot.
    1. Do not double post. It wastes everyone's time.

    2. Do not post in a Forum which is clearly inappropriate for the questions (calculus questions obviously do not belong in a pre-calculus forum).

    3. Show some effort. Show your working and where you get stuck. Do not expect people to do all the work for you. Especially with such a huge list of questions.

    4. Do not post a huge list of questions in the one thread. It can make the thread awkward and difficult to follow.
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