Wednesday, May 8, 2019

calculus - The limit of this function as x approaches 2 from the positive direction (the right).




limx2x24x2





Am I correct in thinking the limit does not exist? Since as x approaches 2 from the right the function increases to infinity and a limit cannot equal infinity. Thanks!


Answer



limx2+x24x2=limx2+(x2)(x+2)x2=limx2+(x2)(x+2)x2=limx2+(x+2)(x2)



Then as you said the denominator tends to 0+ and hence the whole limit tends to +


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