(i) Letf:[a,b]→[a,b] be a continuous function where a.be+ and ab. Prove that there exists a solution for the equation f(x)=x.[3] 相关知识点: 试题来源: 解析Let F(x)=f(x)-x. Notice that F is continuous as well since a difference of continuous functions is continuous. ...
|An−A|=∣∣∣∫ba(f(x+yn)−f(x))g(x)dx∣∣∣≤∫ba|f(x+yn)−f(x)||g(x)|dx.|An−A|=|∫ab(f(x+yn)−f(x))g(x)dx|≤∫ab|f(x+yn)−f(x)||g(x)|dx. Since f(x)f(x) is uniformly continuous, we can pick an NN such that |f(x+yn...
Suppose that F(x):=∫x−∞f(t)dtF(x):=∫−∞xf(t)dt is finite for all xx. Prove that FF is continuous. Ask Question Asked 7 years, 1 month ago Modified 7 years, 1 month ago Viewed 233 times 2 Let ff be a nonnegative, measurable function on RR, and suppose that...
Let f, g be two continuous functions on D. Prove that the functions h(x) = min{f(x), g(x)} and H(x) = max{f(x),g(x)} are continuous on D. Are h and H uniformly continuous on D in f and g ar...
Suppose E(X) = 3 and E[X(X ? 1)] = 28.5. (a) What is E(X2)? [Hint: First verify that E[X(X ? 1)] = E[X2 ? X] = E(X2) ? E(X).] (b) What is V(X)? (c) What is the general relationship among the quantitie ...
Show that the function defined byf(x)={x2sin1/x,x≠00,x=0is differentiable for every value of x, but the derivative is not continuous for x = View Solution Iff(x)={(1+2x)1/x,forx≠0e2,forx=0, then View Solution The function f is given byf(x)=⎧⎨⎩e1/x−1e1/x+...
If y=∣∣∣ ∣∣f(x)g(x)h(x)lmnabc∣∣∣ ∣∣, prove that dydx=∣∣∣ ∣∣f'(x)g'(x)h'(x)lmnabc∣∣∣ ∣∣ View Solution f is a continous function in [a,b]; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x)forx∈[a,b),g(x...
prove: suppose S is a non-empty set having upperbound number set by Archimedes property, for any positive numberαα,exists a integer,it makesλααλααa S's upperbound, while λλ- a ,being not a upperbound to S. so, λα=kααλα=kαα, a upperbound to S ...
Use the definitions of increasing and decreasing functions to prove that {eq}\displaystyle f(x) = x^3 {/eq} is increasing on {eq}(-\infty,\ \infty) {/eq}. Verifying that a Function Is Increasing by Applying the Definition To prove that a funct...
Continuous glucose monitors prove highly accurate in critically ill children Introduction Hyperglycemia is associated with increased morbidity and mortality in critically ill patients and strict glycemic control has become standard ... BC Bridges,CM Preissig,KO Maher,... - Critical Care,14,5(2010-10...