Let f(x) be a differentiable function satisfyingf(x+y)=f(x)+f(y)∀x,y∈Randf′(0)=1.Then Lim_(x rarr0)(2^(f(tan^(2)x))-2^(f(sin^(2)x)))/(x^(3) f(sin x)) equals View Solution Let a real valued function f satisfyf(x+y)=f(x)f(y)∀x,y∈Randf(0)≠0...
Let f be a differentiable function satisfying the equation f(a+b)=f(a)+f(6)+2ab for all a,b∈R. Show that f′(x)=f′(0)+2xLimit Definition of Derivatives:Suppose we have a real-valued function f(x) of one variab...
Let f be a differentiable function satisfying [f(x)]^(n)=f(nx) for all... 03:41 If f (x) =|x-1|and g (x) =f (f (f (x))), then g' (x) is equal to: 03:11 Let F(x)=f(x) g(x) h(x) for all real x, where f(x), g(x), and h(x) are... 03:32 If...
Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for all a, b \in \mathbb{R}. Show that f'(x) = f'(0) + 2x. (Hint: Use the limit definition of the derivative.) Let f(t) be a differentiable ...
Let f : [a, b] → R be continuous. If L is a real number satisfying f (a) <L < f (b) or f (a) > L > f (b), then there exists a real number c ∈ (a, b) with f (c) = L. Uniformly Continuous (Def 4.4.6) Let f : A → R. We say that f is uniformly conti...
Let {eq}f(x)=x^3 + x - 1 {/eq}. Find ech number c in (1,2) that satisfies the conclusion of the Mean Value Theorem. Mean Value Theorem If a function is continuous and differentiable over an interval, then we can apply the Mean Value ...
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Let f(x) is a differentiable function on x∈R, such that f(x+y)=f(x)f(y) for all x,y∈R where f(0)≠0. If f(5)=10,f'(0)=0, then the value of f'(5) is equal to View Solution Let f(x+y)=f(x)⋅f(y) for all x y where f(0)≠0 .If f(5)=2 and f...
Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for all a, b \in \mathbb{R}. Show that f'(x) = f'(0) + 2x. (Hint: Use the limit definition of the derivative.) Suppose f is a differentiab...
Answer to: Let f(x), g(x) be two continuously differentiable functions satisfying the relationships f'(x) = g(x) and f''(x) = - f(x). Let h(x) = ...