The integral
as a limit of sum is
We have
. The sum becomes,
Using the limit as sum,
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint:...
,,tan-ı(-1 + n-2n). 2. Express the limithu 2 as a definite k-1 integral. Make sure to fully justify your work. Hint What is equal to?
,,tan-ı(-1 + n-2n). 2. Express the limithu 2 as a definite k-1 integral. Make sure to fully justify your work. Hint What is equal to?
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...
Express the limit as a definite integral on the given interval.
lim η Σ X; -ΔΧ, +7 [1, 9] (x)2 + = 1 dx 1
i. Explain why this definite integral is an improper
integral.
ii. Determine if this improper integral converges or
diverges. Be sure to treat the improper integral with appropriate
mathematical rigour. Simply treating the improper integral as if it
was a proper integral will result in zero marks. Furthermore, make
sure you clearly explain/justify each step in your limit analysis
working.
thanks for your answer, please give a clear
writing.
(b) Consider the definite integral 2 1 i. Explain why this...
Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1
Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1
Express the limit as a definite integral. n lim Σ 1P10k1 TCK' AXk, where P is a partition of [6, 12] 6 OA. 7x6 dx 12 n B. 7x dx 1 12 Oc. zxdx de 12 OD | 42x2 dx Find the derivative. to y = = S cos Vt dt 0 O A. cos (x3) O B. sin (x3) OC. 6x5 OD. cos (x3) - 1 cos (x3) Solve the initial value problem. dy = x(2+x2)), y(0) = 0...
Express the following limit as a definite integral: 22 3i lim n-+00 2522 n2 1 n2 i=1
Express the following limit as a definite integral. n 1 lim P10 k=1 -Axk where P is a partition of [3,5] 5 The definite integral is si dx. 3
Given R express the limit as n + as a definite integral, that n 3 [:(+9)-3(2+91 5° flade. is provide a, b and f(x) in the expression = b f(x) = Preview
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]