Show that "f(x) = x^3" is continuous on all of ℝ

Solutions

Expert Solution

i have no laptops ,so I have again Handwritten this....I hope this will make you all clear.if you have any doubts again let me know.

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Topology question: Show that a function f : ℝ → ℝ is continuous in the ε...

Topology question: Show that a function f : ℝ → ℝ is continuous in the ε − δ definition of continuity if and only if, for every x ∈ ℝ and every open set U containing f(x), there exists a neighborhood V of x such that f(V) ⊂ U.

show x^1/3 is uniformly continuous on (-infinity,+infinity)

For the following exercises, determine whether or not the given function f is continuous everywhere....f(x) = sec(x) − 3.

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = sec(x) − 3.

Show all your work. Let f(x) = x 5 e x 3 (i) Use the Taylor...

Show all your work. Let f(x) = x 5 e x 3 (i) Use the Taylor series for e x around 0 to find the Taylor series for f(x) (ii) Use (i) to find f (20)(0), f (21)(0), f (22)(0), f (23)(0)

1) Show the absolute value function f(x) = |x| is continuous at every point. 2) Suppose...

1) Show the absolute value function f(x) = |x| is continuous at every point. 2) Suppose A and B are sets then define the cartesian product A * B Please answer both the questions.

f(x)=0 if x≤0, f(x)=x^a if x>0 For what a is f continuous at x = 0...

f(x)=0 if x≤0, f(x)=x^a if x>0 For what a is f continuous at x = 0 For what a is f differentiable at x = 0 For what a is f twice differentiable at x = 0

Define a function ?∶ ℝ→ℝ by ?(?)={?+1,[?] ?? ??? ?−1,[?]?? ???? where [x] is the integer...

Define a function ?∶ ℝ→ℝ by ?(?)={?+1,[?] ?? ??? ?−1,[?]?? ???? where [x] is the integer part function. Is ? injective? (b) Verify if the following function is bijective. If it is bijective, determine its inverse. ?∶ ℝ\{5/4}→ℝ\{9/4} , ?(?)=(9∙?)/(4∙?−5)

Question