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(Solved): Consider the function \[ f(x)=\left\{\begin{array}{ll} 6 \cdot x+7 & x ...
Consider the function \[ f(x)=\left\{\begin{array}{ll} 6 \cdot x+7 & x<-1 \\ -1 & x=-1 \\ x^{2} & -10 \end{array}\right. \] Tick all of the following statements that are correct. \( \lim _{x \rightarrow 0} f(x) \) exists. \( f \) has a jump discontinuity at \( x=-1 \). \( f \) has a jump discontinuity at \( x=0 \). \( f \) has a removable discontinuity at \( x=0 \). \( f \) is discontinuous at \( x=-1 \). \[ \lim _{x \rightarrow-1} f(x)=1 \] \( f \) is continuous at \( x=1 \). \( f \) has a removable discontinuity at \( x=-1 \).
Expert Answer
Given piecewiswe function which is changing for value x=0and?1 1- At x=0 LHL limx?0?f(x)=limx?0?x2=0 RHL limx?0+f(x)=limx?0?(cos?(x)+6)=1