Compute the limit by using known power series
Compute the limit by using known power series 2. lim 30 · (arctan (2) – sin...
8. Compute the limit arctan 2x lim +- X (a) 0 (b) 7/2 (c) –7/2 (d) e (e) 1
Find the limit: sin(30) cos(20) lim 00
3. Calculate the following limit by using the power series of ex 15 3 -e* lim l+x+ 0 24 S х
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
number 4 as clearly as possible
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series...
sin(sin x) Find the limit lim 0-10 sin 2
In the following, we will tse a kmown power series to approximate 1/2 arctan(r) dr to within 0.00001 of the actual value of the definite integral (a) [2pt] Use a known power series representation to express (ctan(x) as a Maclaurin series. What is the radius of the series convergence? 1/2 (b) [4pts] Use your answer from part (a) to express(r) dr as an alternating series (c) [6pts] Your series in part (b) will converge by the Alternating Series Test. (You...
Find the limit. lim (5 sin ?x+ 5 cos?y + sec?z) P(7.7,0) lim (5 sin?x+5 cos?y + sec z) = (Simplify your answer.) P-(7.7.0)
Problem 5: (15 points) (a) Find the limit sin(2x)-2c lim ェ→0 (b)Find the limit lim (sin1/x-/2) ι π /2
Problem 5: (15 points) (a) Find the limit sin(2x)-2c lim ェ→0 (b)Find the limit lim (sin1/x-/2) ι π /2
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y = 0 and yma. 2. Let F(x,y) = sin(x”y), where = sin(u) + cos(u) and y = ew. Use the chain rule (substitution will earn zero credit) to find 3. Find the maximum rate of change of f(x,y) - eat (1,1) and the direction in which it occurs.