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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)...
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...
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...
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...
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
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...
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...
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,...
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...
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 -...
pe sint dt = (A) - tans (B) tan-ls (C) - tan-1 s (D) T - tan-1s (E) None
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
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