which of the following praphs echibit ALL of the listed properties: • im f(a) - -1, • lim () does not extst, • (2) s undefined

Q: |an also converges because 0 If an converges then < lan|, for n = 1, 2, ... n=1 n=1

A:

Q: c). Evaluate: i). ii). limx"y" dxdy. [Verify using Mathematica 00 1 • ₁ (1+x² + y²) ² 00 dxdy.…

A: Verifying using Mathematica: Write this code: Limit[Integrate[x^n*y^n, {x, 0, 1}, {y, 0, 1}], n…

Q: Evaluate the following x-1 2)- limx-o 00~2x²-7x+5

A: To evaluate: limx→∞x3-12x2-7x+5 Solution: Given,limx→∞x3-12x2-7x+5 Here given function is a rational…

Q: for Ea, , if lim a,=0 then the root test fails n = 1 Select one: O True 18 O False

A:

Q: Evaluate lim 3sin4xsin2x म cos2x+1 2

A: This question can be solved by the concept of removing the indeterminate forms in limit

Q: (а-2)п2+4п+1 Find a. b if lim an = 2 for an -). (b-3)п+2 n→∞ O A. 6 Ов. 8 Ос. 10 OD. 12 O E. 20

A:

Q: Find the limits lim 1 as 2 – 4 а. х— 2+ b. х— 2 с. х— -2+ d. x→-2

A: Given, lim1x2-4 (a) x→2+→2+h, h→0 limh→01h2+4+4h-4 limh→01h(h+4)→∞ (b) x→2-→2-h limh→01h2+4-4h-4→∞

Q: |x=1| 1 lim x+1 X-1 A True B) False

A:

Q: Evaluate the following limits. If needed, enter 'INF' for ool and '-INF for -o0. (a) V7 + 9x² lim I…

A:

Q: x+sinx 2. limx00 x+cosx

A:

Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

Q: In x is lim sec 2x x→1 Select one: a. b. T C. 2 d.

A:

Q: 6 — х — 2 Evaluate lim 3 — х — 1 x→2

A: here we use L'hospital rule if limit is  limx→2f(x)g(x) 00 form then we use L'Hospital rule then…

Q: Find lim (a + 2ar + 3ar² + n→∞ .. +nar"-¹) where |r|< 1.

A:

Q: Which of the following statement(s) is TRUE? 1. limr→0+ = 1. x2 1-x2 II. limr→1 does not exist. x-…

A:

Q: Usingthe definitiono lim frak that Lim

A: Given: Limit (1-(1/n^2)) ; n approach infinite

Q: ex - 1 x→0 tanx 7. Find lim A. -1 C. 1

A: The given problem is solved below in detail.

Q: I. lim (-7) = -28 How many of the following are true? II. lim (a? – 4) = 5 x-3 sin x III. lim =D0…

A:

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

Q: 2х -1 The value of lim, is 2x2 +1 1 x→-- 2 a) 3 2 b) - 4 | d) 3. 4 3. 3.

A:

Q: 1-x c) lim- x1 1-Vx 121 sin x d) lim (Hint: Use a calculator to make a table.)

A: c) limx→11-x1-xd) limx→0sin xx

Q: x* +x² 5. lim,-. e* +1

A: