Question

If f is continuous on ( a , b ) and f ( x ) ≠...

If f is continuous on ( a , b ) and f ( x ) ≠ 0 for all x in ( a , b ), then either f ( x ) > ______ for all x in ( a , b ) or f ( x ) < _________ for all x in ( a , b ).

A function f is said to be continuous on the _______ at x = c if lim x → c + f ( x ) = f ( c ).

A function f is said to be continuous on the _______ at x = c if lim x → c − f ( x ) = f ( c ).

When a graph is broken, or disconnected, at a point x = c, the function is said to be _________ at x = c.

A function is ___________ on the open interval ( a , b ) if it is continuous at every point on the interval.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A function f is said to be continuous on the _______ at x = c if...
A function f is said to be continuous on the _______ at x = c if lim x → c + f ( x ) = f ( c ). A function f is said to be continuous on the _______ at x = c if lim x → c − f ( x ) = f ( c ). A real number x is a _______ number for a function f if f is discontinuous at x or f...
Intuitively, a function is _____________ over an interval if its graph can be drawn without removing...
Intuitively, a function is _____________ over an interval if its graph can be drawn without removing a pen from the paper. A function is said to be at continuous on the closed interval [a , b] if it is continuous on the open interval (a , b) and is continuous both on the ___________ at a and on the _________ at b. A real number x is a _______ number for a function f if f is discontinuous at x...
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0...
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0 for every x ∈ [a,b]. 1) Show that either f(x) > 0 for every x ∈ [a,b] or f(x) < 0 for every x ∈ [a,b]. 2) Assume that f(x) > 0 for every x ∈ [a,b] and prove that there exists ε > 0 such that f(x) ≥ ε for all x ∈ [a,b].
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)? If not, why is the function not...
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)? If not, why is the function not continuous? Select the correct answer below: A. Yes B. No, because lim(x,y)→(−1,1)x−yx+y=−1 and f(0,0)=0. C. No, because lim(x,y)→(−1,1)x−yx+y does not exist and f(0,0) does not exist. D. No, because lim(x,y)→(0,0)x2−y2x2+y2=1 and f(0,0)=0.
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
Sketch the graph of a function f that is continuous on (−∞,∞) and has all of...
Sketch the graph of a function f that is continuous on (−∞,∞) and has all of the following properties: (a) f0(1) is undefined (b) f0(x) > 0 on (−∞,−1) (c) f is decreasing on (−1,∞). Sketch a function f on some interval where f has one inflection point, but no local extrema.
For each of the following questions, consider a function, f(x) that is continuous on [a,b]. How...
For each of the following questions, consider a function, f(x) that is continuous on [a,b]. How would you find the critical values of f(x)? Explain. Where would f(x) be increasing/decreasing? Explain. At what possible x values would f(x) have extrema? Explain. Is it possible that f(x) is continuous and has no extrema on the interval [a,b]? Use the Extreme Value Theorem to explain your response. If f’’(c) = 0, c in (a,b), and f’’(x) > 0 for all x values...
Let f(x) be a function that is continuous for all real numbers and assume all the...
Let f(x) be a function that is continuous for all real numbers and assume all the intercepts of f, f' , and f” are given below. Use the information to a) summarize any and all asymptotes, critical numbers, local mins/maxs, PIPs, and inflection points, b) then graph y = f(x) labeling all the pertinent features from part a. f(0) = 1, f(2) = 0, f(4) = 1 f ' (2) = 0, f' (x) < 0 on (−∞, 2), and...
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
consider the function f(x)= -1/x, 3, √x+2 if x<0 if 0≤x<1 if x≥1 a)Evaluate lim,→./ f(x)...
consider the function f(x)= -1/x, 3, √x+2 if x<0 if 0≤x<1 if x≥1 a)Evaluate lim,→./ f(x) and lim,→.2 f(x) b. Does lim,→. f(x) exist? Explain. c. Is f(x) continuous at x = 1? Explain.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT