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Correct inputs for these questions are as follows, although there may be other correct ways of inputting these:

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#### a)

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1. sin(cos({a}x)+{b})
2. \n
3. cos(sin({a}x + {b}))
4. \n
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#### b)

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1. abs((x + {c}) / (x + {d}))
2. \n
3. ln(abs((x + {a}) / (x + {d})))
4. \n
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#### c)

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1. {a}t^({-b})*e^({-c}t)*sin({b}t) + (t + {d}t ^ 3)*e ^ ({c}t)
2. \n
3. arctan(({c}y ^ 2 + {d}) / ((y + {a})*(y + {b})))
4. \n
", "ungrouped_variables": ["a", "c", "b", "d"], "statement": "

FUNCTIONS

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1. The Numbas system recognises all standard functions but you must use brackets for the arguments of the functions, e.g. sin(x) not sinx, ln(a) not lna.
2. \n
3. The absolute value function is written abs(a).
4. \n
5. $\\arcsin(x)$, $\\arccos(x)$ and $\\arctan(x)$ are all recognized as the standard inverse trig functions, and you input them as they are written.
6. \n
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Here are some examples for you to try:

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(If you want help, press Reveal Answers to see correct inputs in the Advice section.)

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Dealing with functions in Numbas.

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Input:

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1. $\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]
2. \n
3. $\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]
4. \n
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Input:

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1. $\\displaystyle \\simplify[all]{Abs((x + {c}) / (x + {d}))}$: [[0]]
2. \n
3. $\\displaystyle \\simplify[all]{ln(Abs((x + {a}) / (x + {d})))}$: [[1]]
4. \n
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Input:

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1. $\\simplify[all]{{a} * t ^ { -b} * e ^ (( -{c}) * t) * Sin({b} * t) + (t + {d} * t ^ 3) * e ^ ({c} * t)}$: [[0]]
2. \n
3. $\\displaystyle \\simplify[all]{arctan(({c} * y ^ 2 + {d}) / ((y + {a}) * (y + {b})))}$: [[1]]
4. \n
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