4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
By using it, show Find the Maclaurin series for sin X. sinx that lim as X → 0 equals X 1.
find the series using the maclaurin series for e^x, sinx, and
cosx
e - cos(x) -isin(ix)
e - cos(x) -isin(ix)
Please answer with work
Evaluate the limit. sin 5x 10) lim 10) X>0 sinx A) -5 B) 1 C) 5 D) 0
Q5 (20 Mark ) Answer the following 1+cOS X a) lim - tan2 x b) Show that dy {tun-'(see x + lan x)} = { cot-'(esex + cotx)] c) Evaluate if ytan't. and x In(t D) att 1. dx العرب عبر العال مع Google مطلقا تو انشاء هذا النمودج داخل Southern Technical University. الأيام عن اسامه استخدام
5. (8 points each) Find the limits: V3x2-6 (a) lim X-00 2x -9X (b) lim x=0x2-sinx COS X (c) lim x X- 2 2
tan2 a then find the minimum value of Vx2 Ifαε 3. 0, X 2
tan2 a then find the minimum value of Vx2 Ifαε 3. 0, X 2
Evaluate the following limits using l'Hôpital's Rule 10. lim sinx-2 x 7x3 10. lime sinti? 11. lim (1-3)* 12. lime e2-1 + 2x 12. lim 24-+2x 0
Question 5 f(x) = esin x Find f'(x). -CO5xesinx 0 -sinx + sinx 0 sinxeỐsinx cosxesinx
[X +61 f(x) = (x + 8) X +6 ,C= -6 uizzes & Tests Ix + 61 Use the graph of the greatest integer function, y = [x], to find the limits given below. Lej (a) lim Le (b) lim 0-3+ e 0--3-