a. Determi n Ma Touries tan form edthe pubeunchin g t) gien by 00 1 <lgl...
1. (14pts) Circle whether the following limit is an
“Indeterminate form” (I) or “Determinate form” (D) andstate the
type of an inderterminate form (0, 1, 0 · 1, 1 1, 00, 10, and 11)
if the limit is an indeterminate form. 0 1
(a) I, D) lim (e -n 3-1-r (b) , D) lm 2 -0 2+1 (c) (I, D) lim o0 1 In(1/2) V (d) I, D) lim (e) (I, D (2:r)3 -1 lim tan (f) (I, D) n(5)...
Prove the following 3,4,5 and 6 in full details?
ges g er tan T 1S aivisible by a prime number. 3. The set of prime numbers is infinite. 4. Merge sort algorithm is linearithmic. 5. The binary search algorithm is O (log n). 6. The Generalized Pigeonhole Principle
ges g er tan T 1S aivisible by a prime number. 3. The set of prime numbers is infinite. 4. Merge sort algorithm is linearithmic. 5. The binary search algorithm is O...
Q9 (Approximation of π) (a)
Show that 1/1 + t2 = 1 − t2 + t4 −
... + (−1)n−1 t 2n−2 + (−1)n
t2n /1 + t2 for all t ∈ R and n ∈ N.
(b) Integrate both side in (a), show that tan−1 (x) =
x − x3/3 +
x5 /5 − ... + (−1)n−1x 2n−1/ 2n −
1 + Z x 0 (−1)n t2n /1 +
t2 dt.
(c) Show that tan−1 (x) − ( x...
3. Find: 7T (1) lim n sin (3) lim arcsin G n-00 n 100 COS- n n00 n 1 (4) lim (1+ (6) lim (n+1 n) n- 3n n-00 1/n (2) lim arctann Vn2 - 1 (5) lim 2n In (1+) (8) lim n (11) lim n+ n 2+1 (14) lim n- 75n+2 (9) lim (nt n-00 700 n->00 n (7) lim V (Vn+1- Vn) (-1)"n (10) lim n+ on+1 (13) lim (3" +5")1/n sinn (12) lim arctan 2n 2n...
t, - 1-4, MA 207
t, - 1-4, MA 207
Use this list of Basic Taylor Series to find the Taylor Series for tan-1(x) based at 0. Give your answer using summation notation, write out the first three non-zero terms, and give the interval on which the series converges. (if you need to enter 00, use the 00 button in CalcPad or type "infinity" in all lower-case.) The Taylor series for tan -1(x) is: The first three non-zero terms are: + + +
The Taylor series converges to tan-1(x) for...
Problem 1 Suppose there is a series of cashflows that lasts n + 1 peri- ods, {at}t, 0 < t <n, and that is growing at constant rate g, i.e. At = (1 + g)tao, Vt. The discount rate is fixed at r and assume g < r. Find an expression for the discounted present value of the cashflows at time 0. Formally, find an expression for S = 20 + 141 + ... + (147) ma al αη 1+r
n : 1 LA + V. Assume that iç (t) = 5 cos(0t – 45°) mA, R, = 1 kN, C, = 1 uF, R= 20 N, and m=1 krad/s. (a) Determine the values of n, and L, that will maximize the time-averaged power delivered to R (b) Find the time-averaged power, P., delivered to R.
Explain why the derivative of g(x) =
1/1+t^2 dt is NOT g'(x) = 1 / 1+x -cos^2 x using FTC1 and the chain
tan x 1 t 2 1 x rule. Find the correct g’(x).
Н tan
pe sint dt = (A) - tans (B) tan-ls (C) - tan-1 s (D) T - tan-1s (E) None