Question

i) show that the function f: Q->Q defined by f(x)=1/((x^2)-2) is continuous at all x in...

i) show that the function f: Q->Q defined by f(x)=1/((x^2)-2) is continuous at all x in Q,but that it is unbounded on [0,2]Q. Compare to the extremal value Theorem.

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
Show that the function f(x) = x^2 + 2 is uniformly continuous on the interval [-1,...
Show that the function f(x) = x^2 + 2 is uniformly continuous on the interval [-1, 3].
1 (a) Let f(x) be the probability density function of a continuous random variable X defined...
1 (a) Let f(x) be the probability density function of a continuous random variable X defined by f(x) = b(1 - x2), -1 < x < 1, for some constant b. Determine the value of b. 1 (b) Find the distribution function F(x) of X . Enter the value of F(0.5) as the answer to this question.
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x)...
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x) /(1+x) is uniformly continuous on (0, ∞) but not uniformly continuous on (−1, 1).
Consider the function f : R → R defined by f(x) = ( 5 + sin...
Consider the function f : R → R defined by f(x) = ( 5 + sin x if x < 0, x + cos x + 4 if x ≥ 0. Show that the function f is differentiable for all x ∈ R. Compute the derivative f' . Show that f ' is continuous at x = 0. Show that f ' is not differentiable at x = 0. (In this question you may assume that all polynomial and trigonometric...
If f is a continuous, positive function defined on the interval (0, 1] such that limx→0+...
If f is a continuous, positive function defined on the interval (0, 1] such that limx→0+ = ∞ we have seen how to make sense of the area of the infinite region bounded by the graph of f, the x-axis and the vertical lines x = 0 and x = 1 with the definition of the improper integral. Consider the function f(x) = x sin(1/x) defined on (0, 1] and note that f is not defined at 0. • Would...
Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The...
Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The graph of f has a vertical asymptote at x=1, and f has a removable discontinuity at x=−2. (a) Show that a=2 and b=−4. (b) Find the value of c. Justify your answer. (c) To make f continuous at x=−2, f(−2) should be defined as what value? Justify your answer. (d) Write an equation for the horizontal asymptote to the graph of f. Show the...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x,...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i by integrating P and Q with respect to the appropriate variables and combining answers. Then use that potential function to directly calculate the given line integral (via the Fundamental Theorem of Line Integrals): a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...
1. Let f be the function defined by f(x) = x 2 on the positive real...
1. Let f be the function defined by f(x) = x 2 on the positive real numbers. Find the equation of the line tangent to the graph of f at the point (3, 9). 2. Graph the reflection of the graph of f and the line tangent to the graph of f at the point (3, 9) about the line y = x. I really need help on number 2!!!! It's urgent!
Which functions fit the description? function 1: f(x)=x^2 + 12. function 2: f(x)= −e^x^2 - 1....
Which functions fit the description? function 1: f(x)=x^2 + 12. function 2: f(x)= −e^x^2 - 1. function 3: f(x)= e^3x function 4: f(x)=x^5 -2x^3 -1 a. this function defined over all realnumbers has 3 inflection points b. this function has no global minimum on the interval (0,1) c. this function defined over all real numbers has a global min but no global max d. this function defined over all real numbers is non-decreasing everywhere e. this function (defined over all...
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1....
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the same for f (2x) and 2f (x). ii) Sketch y = f (x) on the interval [−2, 2]. iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each case, if a solution does not exist, explain. iv) What is the domain of f (x)? b.)Let f (x) = √x −1 and g (x) =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT