Question

In: Advanced Math

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.

Solutions

Expert Solution


Related Solutions

Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2)...
Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2) on the disk D = {(x,y) | x2+y2⩽1}?
Suppose a function f : R → R is continuous with f(0) = 1. Show that...
Suppose a function f : R → R is continuous with f(0) = 1. Show that if there is a positive number x0 for which f(x0) = 0, then there is a smallest positive number p for which f(p) = 0. (Hint: Consider the set {x | x > 0, f(x) = 0}.)
True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x|...
True and False (No need to solve). 1. Every bounded continuous function is integrable. 2. f(x)=|x| is not integrable in [-1, 1] because the function f is not differentiable at x=0. 3. You can always use a bisection algorithm to find a root of a continuous function. 4. Bisection algorithm is based on the fact that If f is a continuous function and f(x1) and f(x2) have opposite signs, then the function f has a root in the interval (x1,...
What is the absolute max / min value for the function f(x) = x sqrt 1...
What is the absolute max / min value for the function f(x) = x sqrt 1 - x on the interval [ 1 , 1 ]
Consider the function and the value of a. f(x) = −2 x − 1 , a...
Consider the function and the value of a. f(x) = −2 x − 1 , a = 9. (a) Use mtan = lim h→0 f(a + h) − f(a) h to find the slope of the tangent line mtan = f '(a). mtan =   (b)Find the equation of the tangent line to f at x = a. (Let x be the independent variable and y be the dependent variable.)   
1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2...
1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2 + 9x + 1 in the following intervals: a) [0,5] b) [-1,2] 2. A company produces and sells x number of calculators per week. The functions for demand and cost are the following: p = 500 - 0.5x and c(x) = 10,000 + 135x. Determine: a) Function of weekly revenue b) Price and number of calculators that have to be sold to maximize revenue...
1. Find the absolute minimum and maximum value of f(x) = x4 − 18x 2 +...
1. Find the absolute minimum and maximum value of f(x) = x4 − 18x 2 + 7 (in coordinate form) on [-1,4] 2. If f(x) = x3 − 6x 2 − 15x + 3 discuss whether there are any absolute minima or maxima on the interval (2,∞) show work please
Find the absolute maximum and the absolute minimum of the function f(x,y) = 6 - x²...
Find the absolute maximum and the absolute minimum of the function f(x,y) = 6 - x² - y² over the region R = {(x,y) | -2 <= x <= 2, -1 <= y <= 1 }. Also mention the points at which the maximum and minimum will occur.
Suppose f(x) is a very well behaved function in that it is continuous and differential everywhere,...
Suppose f(x) is a very well behaved function in that it is continuous and differential everywhere, and that f(2) = 6 and f(6) = 34. a. Find the slope of the line between these two points on the graph. b. What does the Mean Value Theorem tell you about f(x) in the interval between x = 2, and x = 6?
Part A. If a function f has a derivative at x not. then f is continuous...
Part A. If a function f has a derivative at x not. then f is continuous at x not. (How do you get the converse?) Part B. 1) There exist an arbitrary x for all y (x+y=0). Is false but why? 2) For all x there exists a unique y (y=x^2) Is true but why? 3) For all x there exist a unique y (y^2=x) Is true but why?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT