10.7#3

Hey professor, Question wants me to evaluate the limit of the vector as t approaches 0. <(e^(-2t)-1)/t,t^2/(t^3-t^2),3/(17+t)>. I know part of the equation is right and that’s is <x,y,3/17>. I try evaluating the x and y limits and using L’Hospital’s Rule I get the total <0,0,3/17>. The derivative doesn’t work either. How do I evaluate this equation? Best regards,

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L'Hospital's rule is the right way to go for x(t), but you did it incorrectly--so fixing that is the first step of what you need to do. You could use L'Hospital's rule for y(t) too, but you'd have to use it a couple of times because the numerator and denominator both vanish to second order--BUT--that would be too much work because you could just cancel t^2 from the numerator and denominator and that would make getting the limit easy