Differentiability At A Point:A function {eq}f(x) {/eq} is said to be differentiable at some point {eq}x=c {/eq} if the Left-hand derivative and the Right-hand derivative at that point are equal i.e {eq}\lim_{h\rightarrow 0}\dfrac{f(c-h)-f(c)}{-h}=\lim_{h\rightarrow...
Therefore, you can think of a these function as ones that are “more” continuous. They may or may not be differentiable. Uniform continuity doesn’t necessarily imply differentiability.3. List of Continuous FunctionsAll of the following functions are generally continuous:Absolute...
Checking Continuity of a function: This problem involves checking the continuity of a given function. A function is continuous if and only if the left-hand limit is equal to the value of the function at that point which is equal to the right-hand limit of the function. ...
Rolle's theorem is applicable for the functionf(x)=|x−1|in[0,2]. View Solution Verify Lagrange's mean-value theorem for the given functions: (i)f(x)=x(2−x)in[0,1] View Solution Free Ncert Solutions English Medium NCERT Solutions ...
Although it seems intuitive, I don't believe so. Causality depends on differentiability, but not on continuity. Causality refers to the Fed's propensity to supply required reserves in response to deposit expansion or contraction. Differentiability refers to the Fed's ability to make marginal adjustm...
Function, Limits, Continuity & Differentiability, Application of Derivative, Definite Integrals, Differential Equations, Area, Straight Line, Circle , Conic Sections with mixed concept questions. The Numerical Section had lengthy calculations from chapters of Calculus & Coordinate Geometry. A few questions...
For the matrixA=⎡⎢⎣11112−32−13⎤⎥⎦Show thatA3−6A2+5A+11I=O. Hence findA−1 View Solution Check the points where the constant functionf(x)=kis continuous. Check the continuity of functions f(x)={x}^(2)-{x^(2)} at all integral points, where {.} represents...
Check the continuity of the function F(x)={ex−1−x,x≠012,x=0. Piecewise Functions: Continuity Consider a piecewise function given as f(x)={g(x), x≠ah(x), x=a. In order to see whether the function is continuous at point x=a: We have to find th...
How to check the differentiability of a function? A function f fails to be differentiable at a if (check all that apply): a. f has a discontinuity at a. b. f has a cusp at a. c. f has a vertical tangent line at a. d. f...
Class 12MATHSCONTINUITY AND DIFFERENTIABILITYSimilar Questions Check the points where the constant function f(x)=k is continuous. View Solution Check the points where the constant function f(x)= k is continuous View Solution Check the points at which the fixed function f(x)=k Is constant View...