Is the statement true or not true? and why?
"Every function where f(a) and f(b) are opposite in sign, there exists an x-intercept between x=a and x=b."
Is the statement true or not true? and why? "Every function where f(a) and f(b) are...
R such that f is integrable on every [a,b] (6) Suppose f is a function and a where b> a. Then we define the improper integral eb f(x)dx=lim | b-oo Ja f(x)da, if that limit exists. Assume that f(x) is continuous and monotonically decreasing on [0,00). Prove that Joof exists if and only if Σ f(n) converges. This result is known as the integral test for series convergence.
Let f: [a, b] → [a,b] be a continuous function, where a, b are real numbers with a < b. Show that f has a fixed point (i.e., there exists x e [a, b] such that f(x) = x).
Evaluate whether the statement is true or false. Explain why. a. Every point on production possibility frontier (PPF) is Pareto efficient. b. Every Pareto efficient allocation is represented as a point on a utility possibility frontier (UPF). c. If outcome is chosen by Rawlsian social welfare function, sum of utilities will be maximized. d. In pure exchange, the outcome where one consumer has everything is not Pareto efficient.
Question 13 5 pts Which of the following is true for a function f : A + B that is surjective (onto)? a. Rng(f) = B b.every element of B has a pre-image (in A) c. for every y e B, there exists 2 € A such that y = f(x) d. all of the above оа Ob OC d
27. het f(x) be a polynomial function, with f(b) = 3, f(c) = 0, f(d) =1, and fle) -3, and becedce. which is true ? (3 pts) a) x-c is a factor of f(x) b) xtc is a factor of f(x) c) c is likely a touch point d) c is likely a cross point e) there exists n between c and a such that f(n) = 0 f) there exists p between aande such that f(p) = 0
Problem 1: Determine whether the statement is true or false. If the statement is true, then prove it. Otherwise, provide a counterexample. (a) If a continuous function f:R +R is bounded, then f'(2) exists for all x. (b) Suppose f.g are two functions on an interval (a, b). If both f + g and f - g are differentiable on (a, b), then both f and g are differentiable on (a,b). Problem 2: Define functions f,g: RR by: x sin(-),...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable? Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable?
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y).
Determine whether the statement is true or false. If false, explain...
Exercise 1. Let f : R R be differentiable on la, b, where a, b R and a < b, and let f be continuous on [a, b]. Show that for every e> 0 there exists a 6 > 0 such that the inequality f(x)- f(c) T-C holds for all c, x E [a, 히 satisfying 0 < |c-x| < δ