Webuyj limit continuity & derivability - Free download as PDF File (.pdf), Text File (.txt) or read online for free. Question bank on function limit continuity & derivability There are 105 questions in this question bank. Select the correct alternative : (Only one is correct) Q.13 If both f(x) & g(x) are differentiable functions at x = x0, then the function defined as, h(x) β¦ WebMar 22, 2024 Β· Ex 5.2, 10 Prove that the greatest integer function defined by f (x) = [x], 0 < x < 3 is not differentiable at π₯=1 and π₯= 2. f (x) = [x] Letβs check for both x = 1 and x = 2 At x = 1 f (x) is differentiable at x = 1 if LHD = RHD (πππ)β¬ (π‘βπ) (π (π) β π (π β π))/π = (πππ)β¬ (hβ0) (π (1) β π (1 β β))/β = (πππ)β¬ (hβ0) ( [1] β [ (1 β β)])/β = (πππ)β¬ β¦
Continuity - CliffsNotes
WebMay 4, 2024 Β· Continuity and differentiability are properties of a function at a specific point rather than properties of a function as a whole. So the "greatest integer less than or equal to x " function, which is usually written as f ( x) = β x β, is continuous at all points apart from integer values of x. WebMar 6, 2024 Β· Example \(\PageIndex{11}\): Writing a Greatest Integer Piecewise-Defined Function In a big city, drivers are charged variable rates for parking in a parking garage. They are charged $10 for the first hour or any part of the first hour and an additional $2 for each hour or part thereof up to a maximum of $30 for the day. great cornish food shop
[MCQ] The number of points at which the function f (x) = 1/ x
WebLet a β R be such that the function f(x) = ,Ξ±,{cos-1(1-{x}2)sin-1(1-{x}){x}-{x}3,xβ 0Ξ±,x=0 is continuous at x = 0, where {x} = x β [x], [x] is the greatest integer less than or equal to x. JEE Main Question Bank Solutions 2168. Concept Notes 240. Syllabus. Let a β R be such that the function f(x) = ,Ξ±,{cos-1(1-{x}2)sin-1(1-{x}){x}-{x ... WebThe floor function is constant on intervals between consecutive integers and jumps at each integer, so it has a discontinuity at each integer. Thus, $f (x)$ will have a discontinuity at each $x\in (1,2)$ at which $x^3-3$ is an integer. So for what real numbers $x\in (1,2)$ is it true that $x^3-3$ is an integer? Share Cite Follow WebThe greatest integer function is continuous at any integer n from the right only because hence, and f ( x ) is not continuous at n from the left. Note that the greatest integer function is continuous from the right and from the left β¦ greatcornman