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Homepage - MATH 129 SUM20 001 9. DETAILS 2 Consider f(x) cos(x) + 3 √x and...
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
Graphs of functions and are shown below. Suppose x = 0 and x = -1 are vertical asymptotes for both functions. Assume that the graphs continue in the same way as x approaches a 0 and 4(eg stays on top close to = 0, and stays on top close to-). Which of the following statements is TRUE? g(x) f(x). -3 O If 9(x) dx converges, then dar converges too. Isla) na ſs) dx either both 0 The integrals 9(2) dar...
4. [-/10 Points] DETAILS SCALCET8 11.8.AE.002. MY NOTES EXAMPLE 2 For what values of x does the series § (x – 3)" converge? n = 1 SOLUTION Let a, = (x - 3)"/n. Then an + 1 n (x - 3)" 1x - 3 → as n 00. and divergent when x - 3 > Now By the Ratio test, the given series is absolutely convergent, and therefore convergent, when |x - 3|< |x - 3| <1 | <x -...
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...
23. [-16 Points] DETAILS LARCALCET7 4.4.028.EP. Consider the following function. f(x) = 3 sin(x) + 3 cos(x), [0, 27) Find f'(x). f'(x) = Find f'(x). f"(x) = Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.) (x, y) = (smaller x-value) (x, y) = (larger x-value) Describe the concavity. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) concave upward concave downward
Consider f(z32. (a) Prove that f(x)3 - 4z 2 has a root in [0,1] (b) Define a function g(x) such that x is a fixed point of g if and only if it is a zero 2"- of f. (c) Verify that fixed-point iteration with your function g and zo 0.5 will converge (d) Starting with x,-0.5, perform as many iterations as required to find a root of f to 6 decimal places.
1.state the shaded area f(x)=cos(x)+5 g(x)=cos(x)+3 #2. state the shaded area f(x)=sqrt x-4 +3 g(x)=-x+7 Show work as needed. Circle answer. 1. State the shaded area. f(x) = cos(x) + 5 g(x) = cos(x) + 3 2. State the shaded area 1x) = *-4+3 9(4)=-x.7
show steps and explain 9) Determine the value of ... S" (3 sin(x) - 2 cos(x)) (cos(x) + 2 sin(x))da. ... knowing that cos(x) and sin(x) are orthonormal with the weighted inner product <f.9 > 1 . (a)g(x)dr.
Consider the equation f(x) = 2*sin(pi*x) + 3*cos(pi*x) Write a c program that computes the values of f(x) for the following values of x: 0.25, 0.5, 1, 2. Your program should allow the user to enter the value from the standard input and the results will be displayed as follows: /*****************************************************************/ Value of x Value of f(x) 0.25 3.5355 0.5 1 2
Question 4 10 pts #3. Consider the function f(x) = 2 3 (a) (5pts) Find a power series for f(x) centered at 0. (b) (5pts) Determine the interval of convergence of f(x). Upload Choose a File Question 5 10 pts #4. (a) (5pts) Find the Taylor series for f(x) = cos x, centered at 0. (Note: You can refer to the textbook.) (b) (5pts) Using (a), find the Maclaurin series for g(x) = cos(a). Write the first five terms of...