Prove thatxsinxxsinxis continuous for allx∈Rx∈R, using theϵϵ-δδdefinition of continuity. I tried to do this but I get stuck at one point. My attempt: Letx0∈Rx0∈Rand assume0<|x−x0|<δ0<|x−x0|<δ Now consider the following ...
I'm tring to prove ff is uniformly continuous, iff for any infinitesimal {an}{an}, the sequence {f(x−an)}{f(x−an)} is uniformly convergent to ff.I managed to prove the necessity:Assume ff is uniformly continuous on DD, then...
Find the value of f(1) so that the functionf(x)=(3√x2−(2x1/3−1))4(x−1)2,x≠1is continuous at x=1. Which of the following functions are even, and which are odd : (a)f(x)=3√(1−x)2+3√(1+x)2,
Prove that the greatest integer functionf:R→R, given byf(x)=[x]is a many-one function. View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium ...
A function is continuous at point a if ∀ϵ>0∃δ>0 such that |x−a|<δ⇒|f(x)−f(a)|<ϵ.From this we know that the sum, product, quotient and composition of two functions continuous at a is also continuous at a....
Let function {eq}p {/eq} is continuous on {eq}[a,c] {/eq} {eq}M {/eq} is a differential function on {eq}(a,c) {/eq} such that, {eq}\forall \,x \in (a,c),\,\frac{d}M(x) = p(x) {/eq} then, {eq}\int\limits_a^c {p(x)dx = M(c) - M(a)} ...
Prove that the function f :R^2→R defi ned byf(x) =|x|_2/|x|_1 ,if x ≠0f(x)=a,if x = 0.is continuous on R^2\{0} and there is no value of a that makes f continuous at x = 0. 相关知识点: 试题来源: 解析 让x 沿着两条不同的直线趋向原点就行了 ...
13. Prove that the function f(x)=x" is continuous at x =n, where n is a positive integer. 相关知识点: 试题来源: 解析 f(x)=,nN.Here, f(x) is a polynomial function and D= R.Therefore f(x) is continuous at nN. 反馈 收藏 ...
For a function to be differentiable the function must be continuous at respective points. Answer and Explanation: Given value is f(x)=0 For differentiation {eq}\frac{d}{dx}(f(x))=0\\ \frac{d^2}{dx^2}(f(x))=0\\ .\\ .\\ ....
How to prove a function is continuous and differentiable? Show that the function f(x) = | x - 2 | is not differentiable at 2. Show that the function is differentiable: f(x, y) = xy - 5y^2 Use the function to show that f_{x}(0, 0...