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A quiz using Qcmath.

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In answers use function names cos, sin, exp, ln etc.

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Write the mathematical expression for the integral of sin(x) from 0 to b

Correct_answer_1 #

!qcmath 1-cos(b)

Hints_1 #

The integral of sin(x) is -cos(x) + a constant
Answer must contain cos(b)
Answer must contain cos(b) negated
The result is 1-cos(b)

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2

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What is the derivative of ln(x), the natural logarithm of x

Correct_answer_2

!qcmath 1/x

Hints_2

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3

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State a formula for the following power series when the numerical value of q is less than 1: a+a*q+a*q^2+...

Correct_answer_3

!qcmath a/(1-q)

Hints_3

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4

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(This is an example illustrating an important property of QCmath: the restriction that in an answer which is an algebraic expression a function can have only variables as arguments, not expressions - not even numbers).
Write down the partial derivative of y*sin(cos(x)) with respect to the variable x using for cos(x) the notation cx when cos(x) is a function argument

Correct_answer_4

!qcmath -y*sin(x)*cos(cx)

Hints_4

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5

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Write down the formula for the derivative of the fraction x/sin(x)

Correct_answer_5

!qcmath (sin(x)-x*cos(x))/(sin(x))^2

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Qstn_name_number_6

6

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Write an expression in QCmath containing the first three terms of the Taylor series for cos(x) with starting point x = 0

Correct_answer_6

!qcmath 1-x^2/2+x^4/24

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7

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Reduce the expression: (1+2*x^2+x^4)/(1+x^2)

Correct_answer_7

!qcmath 1+x^2

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8

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Write an expression in QCmath for the area under the curve defined by y * exp(-y), with y taking all values between 0 and b

Correct_answer_8

!qcmath 1-b/exp(b)-1/exp(b)

Hints_8

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9

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Write an expression for the 3rd derivative with respect to x of the expression y^2*sin(x)

Correct_answer_9

!qcmath y^2*cos(x)

Hints_9

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10

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Correct_answer_10

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