Evaluate the following limit using Taylor series. 3 lim 2x2 zle x2 1 X>00
Vx+1-1 Evaluate: lim x>0 х Please solve it in detail and show all your steps./
A. Express the limit as a definite integral on the given
interval.
B. Use the form of the definition of the integral to evaluate
the integral.
n Š lim n-> Xi Ax, [1, 3] (xi +13 * 2 i=1 3 6 (2x - x2) dx
All of the following sequences have end behavior lim an = 0. n>00 Get out a clean sheet of paper. Write down all eight sequences, ordered by the speed at which they go to infinity. After you are done ordering them on paper, order them in WebAssign below. Select 1 for the slowest and 8 for the fastest. 10 n1/4 n In(n) n2n n 100 n! ✓n en?
Please answer with work
Evaluate the limit. sin 5x 10) lim 10) X>0 sinx A) -5 B) 1 C) 5 D) 0
Determine if the limit exists, Graphically
b.) lim X1 x2 + 3 2 x<> 1 x=1
Please use formal definitions of tending to infinity and
convergence.. Also, the second limit is lim v_n=L!
Let {Un} and {vn} be sequences of real numbers such that lim un = to n-> and lim = 1 n-> , where l > 0. Determine lim UnUn using definitions of converging to op and converging to a real number. n->
Question 4 4.1 Express the limit as a definite integral on the given integral: 1-x} Ax , [2,6] lim Σ=1 a. (2 Marks) n->00 4+x} lim (?-1 - Ax ,[1,3] (xi) - 4 b. (2 Marks) n->00 4.2 Evaluate the following expressions. Show your calculations. $=1(2p – p2) b. En-o sin a. (2 Marks) пп (2 Marks) 2 C. 2m +2 53 Lm=1 3 (2 Marks) [Sub Total 10 Marks]
Evaluate lim,-_-4+ g(x). 1 1 for -5< x < -4 X + 1 g(x) = 22 for X > -4 1 16 The limit does not exist. 1 3 -4
( 7n3 +1 (1 point) Consider the series > 1. Evaluate the the following limit. If it is infinite, = ( 2n3 + 3) type "infinity" or "inf". If it does not exist, type "DNE". lim vanl = 1 n-> Answer: L = What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: choose one Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent"....