Maths

Question 1

Oblique asymptotes

Answer 1

Rational function when order of numerator
is greater than denominator

Divide out and take limits
Divide numerator by denominator

Question 2

Condition for continuity at f(x) = a

Answer 2

if the left-hand and right-hand
limits are the same there, and if both of these are equal to the value of the function at that point

Question 3

Period of sum of functions

Answer 3

LCM of periods of each function

Question 4

Properties of determinants

Answer 4

All elements in row/column scaled by a factor, determinant scaled by same factor

det(ka) = k^ndet(a)

If positions of two rows/columns interchanged then sign changes

If all elements in row/column are scaled and then added to another row/column no change

If two rows/columns are identical the = 0

If a row/column is zero then = 0

Question 5

Determinants using cofactors

Answer 5

Cofactor of aij = (-1)^i+j x minor of aij