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lets try this problem what is the limit as x approaches zero of the function five x divided by x squared plus two x now we cant use direct substitution here because if we plug in zero were gonna have zero divided by zero which is indeterminate so were not going to do that instead we can evaluate this limit analytically by factoring theres nothing to factor on the top that is on the numerator of the fraction so were not going to change it but in the denominator we can take out the gcf the greatest common factor so if we take out an x x squared divided by x is x and 2x divided by x is positive two now notice that we can cancel an x variable and so well be left with the limit as x approaches 0 of 5 divided by x plus 2. now we can use direct substitution once you replace x with 0 theres no need to rewrite this limit expression now some teachers are picky about this so you have to rewrite it until you replace x with this number so the final answer is 5 divided by 2 thats the limit