solmid1wi01 - MIDTERM I FORM A MATH 132 WI01 I Compute the...

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Unformatted text preview: MIDTERM I, FORM A MATH 132 WI01 I. Compute the following limits (if the limit is + ∞ or-∞ or DNE, state whether it is + ∞ or-∞ or DNE; leave the answer in fractions) (i) lim x →- 3- x x (6 points) Proof. Plug in 0, gives you 3- must be an infinity; check the sign: 3- > so positive; x < 0, since x →- , so the fraction is negative. Hence the answer is-∞ . (ii) lim x →∞ 15 x 7- 9 x 2- 11 x 8- 5 (6 points) Proof. It’s a limit to ∞ , so we need to ignore everything but the highest power of x in the numerator and the highest power of x in the denominator. This gives: lim x →∞ 15 x 7 x 8 = lim x →∞ 15 x = 0 (iii) lim x → 1 x 2- 2 x + 1 x 2 + 3 x- 4 (6 points) Proof. plug in 1, and get: ! so we need to simplify first: x 2- 2 x + 1 x 2 + 3 x- 4 = ( x- 1)( x- 1) ( x- 1)( x + 4) = x- 1 x + 4 so the limit becomes lim x → 1 x 2- 2 x + 1 x 2 + 3 x- 4 = lim x → 1 x- 1 x + 4 = 0 Date : 01/21/2001....
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solmid1wi01 - MIDTERM I FORM A MATH 132 WI01 I Compute the...

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