Study the definition, continuity and differentiability of the limits of the following series. (a)a arctan(nz) Study the definition, continuity and differentiability of the limits of the foll...
1) Use the definition of continuity and the property of limits to show that the function is continuous at x² + 5x the given number a. a = 2 2x+1
please do problems a-c, thank you
1.7 Preview Activity: Limits, Continuity, and Differentiability A function f defined on the interval 4 < x < 4 is given by the graph shown here. Use the graph to answer the questions. a. For each of the values a = -4,-3, -2,-1,0, 1, 2, 3, determine whether or not limf(x) exists. If the function has a limit Lat a given point, state the value of the limit using the notation limf(x) L. If...
help me. ASAP
2. Show that the following limits do not exist 1.2. Limits and Continuity (a) lim(x,y)=(0,0) DEO (b) lim(x,y)=(0,0) 2,2*-*y2 (c) lim (2,3)+(0,0) 4x2-2y2 n(x,y)+(0,0) x2 - 3y2
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...
Homework: Special Limits and Continuity Score: 0 of 3 pts 2.5.49 For what values of a and b is the following function continuous at every x? - 10 XS - 3 f(x) = {ax - b - 3<x<3 x23 For what values of a and b is the function f continuous at every x? a= and b = (Type an integer or a simplified fraction.)
Question 6 (20 points). Determine whether the following series converge or diverge, and by which test: o arctan(k) k-0 oo ok k! k-0
Question 6 (20 points). Determine whether the following series converge or diverge, and by which test: o arctan(k) k-0 oo ok k! k-0
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...
U Prove the following statement using the definition of limits and illustrate with a diagram. (10pts) lim (3x + 1)-2 1 (4pts) Part 1: Find 8 (3ptsi Part 2 ВАМ НЕКА Зpt)
n-arctan(n) We want to use comparison test in order to determine whether the series is convergent or divergent. Which of the following is correct? n=2n2n+2n +5 Select one O a. It is divergent by comparison test with the series nen O b. It is convergent by comparison test with the series SIS M8 n c. It is divergent by comparison test with the series n=1nn о d. It is convergent by comparison test with the series 1n2 e. It is...