00 1 for convergence. It turns out that a good 7. Suppose that we want to...
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...
an converges. 6. We want to use the Integral Test to show that the positive series All of the following need to be done except one. Which is the one we don't need to n=1 do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = an for all n. (b) Show that ſi f(x) de converges. (C) Show that lim f(x) dx exists. t-00 (d) Show that lim sn exists....
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
1- 2- Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in Jerez 42 + ex dx for which the derivative is also present. We see that 42 + ex is part of this integral, and the derivative of 42 + ex is ex et which is also present....
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -VX dx & e Step 1 - b е e 504 47 dx = lim b→ Ji 47 dx can be evaluated using the substitution u = x and VX 1 du = dx. 2V 2. Step 2 When x = 1 we have u = 1 and when x = b, we have b Vb Step 3 So lim b→ os 47 e...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of f(x) at x = x = -5. (a) The nth derivative of f(x)is f(n)(x) = 8(7)^ne^(7x) At = -5, we get f(n)(-5) = 8(7)^ne^-35 (c) The Taylor series at x = -5 is too T(x) = (3/7^n](^-35)n!/(n+ (x + 5)” n=0 (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+oo 1/(x+1) |x + 51 an and so...
9.3 Integral Test & Seric Use the Integral Test to determine the convergence or divergence of the series. 2 3n + 6 n = 1 Part 1 of 5 Recall the Integral Test. Iff is positive positive, continuous, and decreasing decreasing for x 2 1 and an = f(n), then an and f(x) dx either both converge or both diverge. n=1 Part 2 of 5 Let f(x) 2 3x + 6 Note that f(x) is positive, continuous, and decreasing for...
please i need final answers just just put option and write answer don t need to solve need it asap please thanks Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer. rdx ſ dx Choose the correct answer below. OA. 1 By the Direct Comparison Method, converges because Os s +4 a on 3, 00) and x dx converges. x +...