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Calculus

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This is my first calculus class and I am lost on how to answer these. The book isn't giving me a clear explanation for help. Any help someone could provide would be great!

1. Use a reference triangle to find the given angle.
cos -1 (1/2) give an exact answer in terms of pi

2. Express In 0.25 in terms of In 2 and In 3. Simplify your answer. Use integers or fractions for any number in the answer.

3. Determine whether the function is even, odd or neither.
f(x)=4x^5 + 3x^3

Thank you!!!!

  • Calculus - ,

    1. Use a reference triangle to find the given angle.
    cos -1 (1/2) give an exact answer in terms of pi

    adjacent/hypotenuse = 1/2
    well, if you know about 30,60,90 triangle the answer is immediate.
    sin 30 degrees = 1/2
    cos 60 degrees = 1/2
    60 degrees = pi/3 radians

  • Calculus - ,

    2. Express In 0.25 in terms of In 2 and In 3. Simplify your answer. Use integers or fractions for any number in the answer.

    ln (1/4) = ln 1 - ln 4 = 0 - ln 4

    -ln 4 = -2 ln 2

  • Calculus - ,

    3. Determine whether the function is even, odd or neither.
    f(x)=4x^5 + 3x^3

    For negative x, this function is negative of the corresponding value for positive x
    Therefore it is ODD
    In general odd powers of x are odd and even powers of x are even
    eg
    f(x ) = +x
    f(-x) = -x odd

    f(x ) = + x^2
    f(-x) = + x^2 even

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