Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. lim...
Pls explain very carefully (state the thm u use in approriate part) 5. Limits of integrals Compute the following limits and justify the calculations: sin (x/n) dx 5. Limits of integrals Compute the following limits and justify the calculations: sin (x/n) dx
2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx. 2. (a) Suppose that f is Lebesgue integrable on R. Find the following limit: n sin(x/n f(x) dz. (b) Find the value of the limit in the special case: linn onsin(x/n) n→oo/.oo X(X2 + 1) dx.
DO NOT use a calculator. Exact answers only, no decimals. 1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr 1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
-0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote 1 - cos(8x) lim x+01 – cos(7x) 8x – 7* – 1 lim x² - 1 Answer(s) submitted: toy (incorrect) 9. (1 point) Compute the following limit using l’Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote -0. lim 7 sin(x) ln(x) = x ot Answer(s) submitted:
1. Determine the following limits, algebraically where possible. x 2020 + sin(x) c) lim 1.001"
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)! (-« <...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
1. Compute the following limits algebraically, if possible: 4.2 +1-3 (a) lim 5.2 – 1 (b) lim 2 - 2 100 3.42 - 2.c 2 (c) lim csc(7x) sin(4x) (d) lim lim (1+3) 20 22 (e) lim +01 – COS X