1. Use the Limit Comparison Test to prove that the series S(a, b) converges unless a or b is a negative integer. Why must this restriction on a and b be imposed? 2. In all that follows we assume with...
2. Prove that the infinite series Ex=1(-1)k diverges. (Hint: Compute the first few terms of the sequence of partial sums and determine a formula for the nth partial sum, Sn. Using this, give a formal proof, starting with the definition for divergence of this series. (Additional reference: Workshop Week #7)
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
Solve the taylor series and include every steps. I. (a) Use the root test to find the interval of convergence of Σ(-1)4. (b) Demonstrate that the above is the taylor series of _ by writing a formula for f via taylors theorem at a = 0. That is write /(z) = P(z) + R(z) where P(z) is the nth order taylor polynonial centered at a point α and the remainder term R(r)- sn+(e)(-a)t1 for some e 0 O. Show that...
1) 2) 3) 4) 5) (a) Find the limit of the sequence whose kth term is sirk) Confirm your answer graphically, and show your graph for full credit. (6) Let be K + 4k 3k? + 7 k + 8 If the sequence {b} converges, find its limit. Use formulas for finite geometric series and infinite geometric series to find exact answers for each of the following: т S 6 and NED 205 Use vertical rectangle slices to write a...
all but dont work on the julia box one which is 2 i think so 1-3-4 Fitchburg State University Department of Mathematics Project #3 Math 2400: Calculus II April 11, 2019 project for Calculus II. You may work on this with up to one other fellow student. Answer all questions completely and type or neatly write out. The final project should be turned in by Tueeday, April 23. How is it that we generate For this project it helps to...
1 10 onvelge a636lutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. (1n(b) n7/3-4 (2k)! n-2 k-0 (-1)k 2k 4. (a) (10) Let* Find a power series for h(), and find the radius of convergence Ri for h'(x). Find the smallest reasonable positive integer n so that - (b) (10) Let A- differs from A by less than 0.01. Give reasons. 5. (a) (10) Let g(x) sin z. Write down the Taylor series for...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us first consider a point mass m > 0 with a spring k> 0 (see Figure 23.52). This system is sometimes called a simple harmonic oscillator. The equation of motion (EMI) is given by ma= -kr (1) where the acceleration a is given by the second derivative of the coordinate r with respect to time t, namely dr(t) (2) dt de(t) (6) at) (3) dt...
1. According to the paper, what does lactate dehydrogenase (LDH) do and what does it allow to happen within the myofiber? (5 points) 2. According to the paper, what is the major disadvantage of relying on glycolysis during high-intensity exercise? (5 points) 3. Using Figure 1 in the paper, briefly describe the different sources of ATP production at 50% versus 90% AND explain whether you believe this depiction of ATP production applies to a Type IIX myofiber in a human....