thankYou Express the limit as a definite integral n lim Σ ( sec c?q)4 Axk, where P is a partition of [-67, 6x] ||P|| → 0k=1 6 on secx 12x dx 6 1 ов. | | sec x ds oci tan x dx 6 6 00 1 sec ? x dx 6 Use the graph to evaluate the limit. OA. 2 lim f(x) OB. 0 X0 C. - 2 Ay O D. The limit does not exist. 5 4 3...
i need help with #6, #15, and # 17. please and thank you! 1 lim 8 lim- 22 2 lim Problems for $1.3 For problems 1 through 14: By replacing functions with a few terms of their asymptotic series, find the following limits. et - 26 +1 tan(x) – sin(x) cosh(x) 20 cos(2) - 11 - 22 9 lim sin(x) sin (x) – 2,2 1-0 24 *+0 tan(x) tan-(x) - 22 3 lim x2 + x -2 10 lim x1...
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+ 40 Show the following results. 1-e2...
Q-2: a) Find the limts of: 1: lim (x cotx) sin 7x 2: lim 4x x²+x-2 3: lim x-x (9 marks) b) Find the derivative of the functions: 1- y= In tanh 2x 2- y = cseh (x+1) (6marks)
QUESTION 8 Evaluate the integral. dx Vx2 - 10x + 21 x-10) sin + C 2 X-5 tan +C 2 2 sin -1 X-5 2 +C x + 5 sin! + 2
find the limits analytically, show all steps x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
1. Suppose that lim x) = A, lim f(x) = B, 0) = C, where A, B, C are distinct real numbers. In each of the following, fill in the corresponding box by: • Expressing the limit in terms of A, B, C if it is possible to do so using the given information; • Writing DNE if it is possible to conclude that the limit does not exist using the given information; • Putting a X. otherwise. No explanation...
Question # 1. (6 marks) (a) Determine whether the following integral converges or diverges. L". tan(34) de (b) Determine whether the following integral converges or diverges. 8 dar ſi VE – (2+sin() (c) Consider the function, f(x) = 3-*, by computing each, determine which has a greater value, ſin(81) 5 (7)de or 5f(n)
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....
Use the graphs to identify the values of c for which lim f(x) does not exist. (Enter your answers as a comma-separated list.) 5 4 3 1 X 1 2 3 4 5 -5 -4 -3 -2 -1 -1 -2h (b) 21 -6 -2 Consider the following function and graph. f(x) = 8 + -10-8-6-4-2 2 4 6 8 10 -2 Determine whether f(x) approaches oor - as x approaches 2 from the left and from the right. (a) lim...