17. If a function f(x) is differentiable at x =c, prove that it is continuous at x = c. 相关知识点: 试题来源: 解析Since fis differentiable atc. we have i lim_(x→c)(f(x)-f(c))/(x-c)=f'(c) But for, we have x≠qc f(x)-f(x)=
A function f(x) is differentiable in and f' is continuous in .Use Fundamental Theorem of Calculus to evaluate:a) f'b) f' 答案 a) b) 相关推荐 1A function f(x) is differentiable in and f' is continuous in .Use Fundamental Theorem of Calculus to evaluate:a) f'b) f' 反馈 收藏 ...
Answer to: Determine whether the statement, if a function is differentiable at point (a, f(a)), then f(x) is continuous at x = a, is true or false...
Step by step video & image solution for If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that cf^(prime)(c)-f(c)=0 cf^(prime)(c)+cf(c)=0 f^(prime)(c)-cf(c)=0 cf^(prime)(c)+f(c)=...
Explain.Continuous and Differentiable Functions:Let f be a function of real numbers and let a point c be in its domain, if there is a condition that, limx→cf(x)=f(c) Then the function is called continuous at c . Also, if left hand limit and right-hand li...
【题目】 A function f(x) is differentiable in (-∞,∞) and f' is continuous in (-∞,∞).Use Fundamental T heorem o f Calculus to eva luate:a$$ \frac { 1 d } { 1 a x } $$)$$ ( \int _ { x } ^ { x ^ { 2 } } f ( t ) , t $$)b)$$ \int _ { x } ...
( ) A. $-4$ B. $-2$ C. $1$ D. $4$ 答案 D相关推荐 1$f$ is a continuous, differentiable function represented in this table. Given $g(x)=f(x^{2})$, find $g'(2)$. ( ) A. $-4$ B. $-2$ C. $1$ D. $4$ ...
Let f be the continuous and differentiable function such that f(x)=f(2-x), ∀x∈R and g(x)=f(1+x), then Ag(x) is an odd function Bf(x) is an even function Cf(x) is symmetric about x=1 DNone of the aboveSubmit If a function f satisfies the conditions f(x+y)=f(x...
From here we have that if a function isn't continuous it is differentiable. Answer and Explanation:1 (a): Since we have: limx→2−f(x)=0,limx→2+f(x)=−2 And because:0≠−2we conclude that the... Learn more abo...
The function f(x) = x^{1/3} is differentiable at x=0. (a) True (b) False State true or false. If it is false explain why. If f (x) is differentiable at x = c, then f (x) is continuous at x = c. True/False. If f is differentiable at c, then ...