Find the constant 'a' such that the function is continuous on the entire real line. g(x) = 7sin xx if x < 0 and g(x)=a−8x if x≥ 0. a=? Continuity in a Function: The continuity of the function is defined with the graphical a...
Determine whether the function is continuous at the indicated value ofx. f(x)=ln|x+3|atx=−3 Absolute Value Functions: Suppose a function isy=|x|; so,y=−xifx<0. Andy=xifx>0. So,yis always positive. Similarly, ify=|x−a|, it isy=(x−a)i...
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = {(x + 2{x^3})^4}, a = - 1Use the definition of continuity and the properties of li...
The function f(x, y)=(x y)^(1/3) is continuous on ^2 since it is a composition of a polynomial and the cube root function, both of which are continuous. (See the text just after Example.)(array)lf_x(0,0)=limlimits _(h → 0) (f(0+h, 0)-f(0,0))h=limlimits _(h ...
If the function f is continuous for all real numbers and if f(x)= (x^2-4)(x+2) when x≠q -2, then f(-2)= () A. -4 B. -2 C. -1 D. 0 E. 2 相关知识点: 试题来源: 解析 A limlimits _(x→ -2) (x^2-4)(x+2)=limlimits _(x→ -2) ((x+2)(x-2))(x+2...
Question: Show that the function f(x) is continuous over R. a) f(x)={1−x2lnx if x≤1 if x>1 b) f(x)={sinx if x<4πcosx if x≥4π Under what conditions is the following function f(x) continuous for all real numbers. ...
The function f(x)=e−|x| is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these A 1 B 2 C 3 D 4 Video SolutionText SolutionVerified by Experts The correct Answer is:DWe have f(x)=e−[x]={exx<0e−xx...
The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 (b) continuous and differentiable everywhere (c) not continuous at x=
()=\((array)l()^3-9;<2 210;=2 (3(-2)(^2)();> 2(array). ( ) A. Yes, because the limit exist. B. Yes, because the value and the limit are equal. C. No, because the value and the limit are not equal. D. No, because the value and the limit are equal....
Determine whether function is continuous at x= 3. If discontinuous, identify the type of discontinuity as infinite, jump, or removable.f(x)=(cases) 2x&(if)&x<3 9-x&(if)& x≥3 (cases) 相关知识点: 试题来源: 解析 continuous 结果一 题目 Determine whether is continuous at x=3. If...