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Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

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Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires integration by parts.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

More work on differentiation with fractional coefficients.

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Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Calculate the expression $\frac{12}{4}a+\frac{3}{5}a$. One of the following is not correct, which one?

Given value of x^(1/n), x^(-1/n) find x.

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More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers