Continuity and Differentiability
Prove that the function f(x)=5x−3is continuous at x=0, at x=−3and at x=5.
Let f be a continuous function defined onto [0,1] with range [0,1]. Show that there is some c in [0,1] such that f(c)=1−c
Discuss the continuity and differentiability of f(x)=∣x+1∣+∣x∣+∣x−1∣∀x∈R; also draw the graph of f(x)
The right hand derivative of f(x)=[x]tanπxatx=7 is (where [.] denotes the greatest integer function) 0 b. 7π c. −7π d. none of these
let f(x)=x3−x2−3x−1,g(x)=(x+1)aand h(x)=g(x)f(x) where h is a rational function such that (1) it is continuous everywhere except when x=−1,(2)x→∞limh(x)=∞ and (3)x→−1limh(x)=21 then the value of h(1)