solve 2-3 1. Use a Taylor series to get the limit: In(x+3) 2. Use a Taylor series to get the derivative of f(x) = arctan x and check for the interval of convergence. Is the interval of convergence for f' the same as the interval for for different? Why? 3. Use a Taylor series to solve y' (t) - 3y = 10,y(0) = 2
Evaluate the following limit using Taylor series. -X- In (1 - x) lim x→0 106² - x - In (1 – X) lim (Simplify your answer.) x→0 1082
Use Taylor polynomials to evaluate the limit. e-3x – 1 7) lim X0 х sin 2x - sin 4x 8) lim x>0 х
Evaluate the following limit using Taylor series. 3 lim 2x2 zle x2 1 X>00
hw help Use L'Hospital's rule, if applicable to find the limit. x3-27 lim- * +3 e*2-9-1 Select the correct answer. 0 27 ООО DNE or Use L'Hospital's rule, if applicable, to find the limit In(3x2+5) lim X3-7 X00 Select the correct answer. DNE or 00 5 3 -7 Solve the following limit using any valid method. x3 + 9 lim *** in (X? + 6) DNE or o 1 انہتا
In(z) 3, Consider the function f(x)= (a) Find the Taylor series for r(z) at -e. b) What is the interval of convergence for this Taylor series? (c) Write out the constant term of your Taylor series from part (a). (Your answer should be a series!). (d) What can you say about the series you found in part (c), by interpreting it as the limit of your series as x → 0. (Does it converge? If so, what is the limit?)...
solve please now Evaluate the following limit using Taylor series. 8 tan* *(x) – 8x+x lim x³0 33³ 8 tan (x) – 8x + x2 lim X-0 = (Simplify your answer.) 3x
QUESTION 3 Use the graph to find the limit, if it exists. lim f(x) =[a] x + 1 3(x) co . - 2 - -1 -27 QUESTION 4 Use the graph to find the limit, if it exists. 4 lim XO 1 2+ex =[a] 2 - 2 QUESTION 5 Use the graph to find the limit, if it exists. lim tan X = [a] XT/2 Fla T 1
lim X3 ws #1 use E-s limit definition to prove #2 Find an equation of the tangent line at (1,1) on the curve y4+xy =X3_x+2.
3. Limits. The limits below do not exist. For each limit find two approach paths giving different limits Calculate the limits along each path. You may want to use Taylor series expansions to simplify the limits. sin (x) (1-cos (y) a) lim (y)(0,0 x+ PATH 1: LIMIT 1 PATH 2: LIMIT 2 b) lim (y)(8,0) cosx + In(1+ PATH 1: LIMIT 1 PATH 2: LIMIT 2 3. Limits. The limits below do not exist. For each limit find two approach...