Week 3

Question 1

Triangle inequality

Answer 1

abs(x + y) is smaller or equal to aBS(X) + abs(y)

Question 2

abs(x)^2

Answer 2

x^2

Question 3

abs(xy)

Answer 3

abs(x)abs(y)

Question 4

derivative from first principles

Answer 4

equation thing, yk it

Question 5

A function f(x) can fail to be differentiable at x = a in 3 ways:

Answer 5

the function has a ‘corner’ or ‘kink’ at x = a
the function is discontinuous at x = a
the function has a vertical tangent line at x = a

Question 6

how to check for differentiability if continuous function changes form at a

Answer 6

see if left and right hand limits about a match

Question 7

indeterminate forms

Answer 7

can be of type 0/0 (try factor and cancel) or inf/inf (divide by highest power of x)

Question 8

lhopitals rule

Answer 8

lim f(x)/g(x) = lim f’(x)/g’(x) applies to side limits and limits to infinity