(c) lim zé csc z. 2-0
1. Evaluate each of the following limits: (4 pts ea) b) lim 2- a) lim VF-1 bilim 7-x
-4x+1 1) (15 pts) Evaluate lim X-V1672+5
4. (10 pts) Evaluate the following limits: (a) lim h0 16+h - 4 h (b) limusin 10
Solve by using complex variables. L'Hospital's Rule 3.78. Evaluate (a) lim 2z2+(3-40z-6i, 3.79. Evaluate (a) lim 22 +4 (b) zlim3 (z-em/3)(Z3 1), (c) lim za+2+1' z sin z (b).li.u--.n(2) xm Evaluate sin 2
5a) (5 pts) Find lim inf (xn) and lim sup (rn), for rn = 4 + (-1)" (1 - 2). Justify your answer 5b) (5 pts) Find a sequence r, with lim sup (xn) = 3 and lim inf (x,) = -2. 5c) (10 pts) Let {x,} be a bounded sequence of real numbers with lim inf (x,) = x and lim sup (x,) = y where , yER. Show that {xn} has subsequences {an} and {bn}, such that an...
Evaluate 4 cot – 3x csc 4x dx.
Evaluate the integral. 5/6 6 csc 6 cot e de /6 5/6 s 6 csc ecot de x/6 (Type an exact answer, using radicals as needed.)
Question 13 0.14 pts Use L'Hospital's rule to evaluate In(x + 1) – lim 1 cos(3x) 20 1 9 1 0 On 1 3 O -1 0
6. Use l'Hopital's rule to evaluate the following limits 1+cos (Te sin(z) (a) lim z-+0 log (-1) (b) lim 92I-2 cos(TI) (c) lim r sin Page 2 of 2 0 words