- #1

doktorwho

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## Homework Statement

Give the example and show your understanding:

[1][/B].Lets define some property of a point of the function:

**1.**Point is a stationary point

**2.**Point is a max/min of a function

**3.**Point is a turning point of a function

If possible name a function whose point has properties of being:

a) 1&2

b) 2&3

c) 1&3

d) 1&2&3

**[2].**Give examples of a sequence ##{c_n}## that has these properties:

a) The limit of a sequence is +∞

b) The sequence has limit of 0 but can be separated into 2 sequence products of which one diverges

c) The sequence is divergent with at least one of its limits going to +∞

**[3].**Name a function and an interval on which it is (if possible):

a) Continuous and unbounded

b) Continuous and Bounded

c) Discontinuous and Unbounded

d) Discontinous and Bounded

e) Unbounded and differentiable

f) Bounded and differentiable

g) Unbounded and undifferentiable

i) Bounded and undifferentiable

## Homework Equations

3. The Attempt at a Solution [/B]

Here are my examples for all 3 parts and i would really appreciate your feedback on each.

[1].

a) ##f(x)=x^2##

b) [could not find such function, is this even possible?]

c) ##f(x)=x^3##

d) [same as with the b), i could not find one. I tried ##cosx## but its turning point is not its max]

[2].

a) ##c_n=n##

b) ##c_n=\frac{\sin x}{x}##

c)##c_n=(-2)^n##

[3]

a) ##f(x)=x## (R)

b) ##f(x)=\arcsin x## [-1,1]

c) ##f(x)= 1/x## not sure about the interval, maybe [-1,1]

d) could not find

e) ##f(x)=x## on R

f) ##f(x)=1/x## on [-1,1]

g) could not find

i) could not find

Appreciate it, thanks.

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