x+1=0

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Examine the continuity of the following function at the given point : f(x) = {(1 + x, x 0),(1, x = 0):} at x = 0.

f (x) = {{:((|x^(2)- x|)/(x^(2) - x),xne 0"," 1),(1",", x = 0),(-1",", x = 0 ):} is continuose for all :

f (x) = {{:((|x^(2)- x|)/(x^(2) - x),xne 0"," 1),(1",", x = 0),(-1",", x = 0 ):} is continuose for all :

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}

Find the value of x if, /_\ = |[x^(2),1,x],[0,3,-1],[x,-1,1]|=0

Assertion (A) : Lt_(x to0) (x)/(1+e^((1)/(x)))=0 Reason(R) : As x to 0, e^(1//x) to0 and x to 0+,e^(-1//x) to 0

x^(5)-1=0X5-1=0

If f(x) =("In"x)/x "then" |{:("In"x,x,0),(1//x,1,x),(-1//x^2,0,2):}| is

Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,x=0]:} at x=0.