Ben Brawn

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

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Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

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Just what the title says, I guess.

Just what the title says, I guess.

Just what the title says, I guess.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Seven standard elementary limits of sequences. 

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

Test whether a student knows the root test of a series, and how to use it. Series include those that the root test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

Graphing $y=ab^x+c$

Basic question on limit laws and the squeeze theorem for sequences.

Determine a finite sum and a limiting sum of a geometric series written using sigma notation. I'm not sure how to eliminate rounding errors...

Often students need practice re-indexing series, these are three questions that give them that opportunity.

Test whether a student knows the divergence test of a series, and how to use it. Series include those that the diverence test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

This question tests to see if students can recognise a $p$-series and based on its $p$-value determine if it is convergent or divergent.

This question tests to see if students can recognise a geometric series and based on its common ratio determine if it is convergent or divergent.

This question tests to see if students can recognise an alternating series and based on the alternating series test and the divergence test determine if it is convergent or divergent.

At the moment there is no example included with $b_n\rightarrow 0$ which isn't eventually monotonically convergent. 

Test whether a student knows the ratio test of a series, and how to use it. Series include those that the ratio test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

Test whether a student knows the comparison test of a series, and how to use it. Series include those that the comparison test is inconclusive for.

Test whether a student knows the monotonic sequence theorem.

Recognising the equation of a semi-circle centred at the origin. Top, bottom, left and right.

Graphing exponentials with a base between 0 and 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

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Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

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