1.

We want to compute 32 lim I-+00 V/724 +1 a) At : approaches 00, we get an indeterminate form of the type ( 190 0 00/00 0 0 x 00 0 0/0 O co - 00 0 00 3 b) By factoring from the numerator and denominator appropriately, rewrite in the form where V/724 +1 V7+ g(I) 9(I) = c) Compute lim g(I). I-+00" Answer: 3 d) To compute the limit in (e), we must use the fact that h(y) = is continuous at a certain point y. V7ty Answer: y = 372 e) Using your results in (c) and (d), compute lim V/724 +1 Answer:We want to compute the following limit 4t lim t-+0 5- 25 + 6t a) As t approaches 0, this gives an indeterminate form of the type O 190 0 0 x 00 0 00/00 0 0/0 0 co-00 0 00 4t We consider the function f defined by f (t) = for t *0. 5 - V25 + 6t Since we are faced with an indeterminate form, we need to simplify f(t) before evaluating the limit b) Select which strategy you will use to simplify f(t): O Rationalization O Partial fraction decomposition O log transformation O Factoring c) Simplify f(t) using the chosen method on b) so that your simplified function isn't an indeterminate form as t approaches 0. The simplified form of f(t) = d) Using your simplified form of f(t), compute the limit: 4t lim t-+0 5 -,25 + 6t