Class 12

Math

Calculus

Continuity and Differentiability

Find all the points of discontinuity of the function f defined by$f(x)={x+2,ifx1$

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What value must be assigned to $k$ so that the function $f(x)={x−4x_{4}−256 ,x=4andk,x=4$ is continuous at x=4.

If $f(x)={sinx2 x=nπandn∈I_{2}x=nπ $ and $g(x)=⎩⎨⎧ x_{2}+145 x=0x=0x=2 $ then $x→0lim g{f(x)}$ is

If the function $f(x)=(32+bx)_{51}−2(128a+ax)_{81}−2 $ is continuous at $x=0$ , then the value of $ba $ is (A) $53 f(0)$ (B) $2_{58}f(0)$ (C) $564 f(0)$ (D) none of these

Number of points of discontinuity of $f(x)=[sin_{−1}x]−[x]$ in its domain is equal to (where [.] denotes the greatest integer function) a. 0 b. 1 c. 2 d. 3

Which of the following functions is not continuous $∀x∈R?$ $2sinx+3 $ (b) $e_{x}+3e_{x}+1 $ $(2_{3x}+52_{3x}+1 )_{75}$ (d) $sgnx+1 $

Discuss the continuity of $f(x)=sgn(x_{3}−x)$

A twice differentiable function f(x)is defined for all real numbers and satisfies the following conditions $f(0)=2;f_{′}(0)−−5andf(0)=3$. The function $g(x)$ is defined by $g(x)=e_{ax}+f(x)∀x∈R$, where 'a' is any constant If $g_{′}(0)+g(0)=0$. Find the value(s) of 'a'

If $f(x)={(π−2x)_{2}2cosx−sin2x ,x≤2π 8x−4πe_{−cotx}−1 ,x>2π $ , then which of the following holds? (a)$f$ is continuous at $x=π/2$ (b)$f$ has an irremovable discontinuity at $x=π/2$ (c)$f$ has a removable discontinuity at $x=π/2$ (d)None of these