Let CR" be an open set on which f is locally integrable. Tony is computing the improper integral fdv. fdV. He has fixed a single specific exhaustion (k) kEN of the domain and computed lim 1₁.₁ k→∞ Consider the following statements: S (A) IF f≥ 0 on S, THEN (B) IF I fav (C) IF lim Ja k→∞ √ Sk (D) IF lim k→∞ (E) IF lim k→∞ O (A) (B) (C) (D) (E) | lim / = lim fdv I fav f dv f dv = ∞, THEN = = = ∞, THEN f dᏙ . fdV, THEN f> 0 on 2. Sa Which of the above statements are necessarily true? Please select ALL statements that are correct. lim kj [fav [fdV diverges. 237, THEN / fdV converges. = x.

Q: 2) Use "TELESCOPE technique" to find x which is involved in INFINITE PROCESS. 4 4 4 4 4 4 4 X = 42…

A:

Q: such f(2x)-f(x) = = b x 1) than f'(x) is alsa a-b 6. f(x) is differentiable On [0,00), lim f'(x) =…

A: Given that, f(x) is differentiable on [0,∞) and limx→∞f'x=b We have the expression, limx→∞f2x-fxx=b…

Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: 8. Use the alternate form of the denivative: lim f(x)-flc) to show that f(x) = | x + al %3D X→し is…

A:

Q: Va² –3 –2 \, x2+1 lim x→-1

A: Given: limx→-1x2-3-2x2+1

Q: 5. Determine the infinite limit. a). f(x) = lim +1 x-5 2-t b). ƒ(t) = lim t→1 (t–1)2 x→5-

A:

Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: Evaluate the limit 7(y² – 1) - lim 3y²(y – 1)3 y→2

A:

Q: Use the definition of limit to prove lim (r+ 4y²) = 6. (2,y) (2,1)

A:

Q: 2 lim x→1- x²

A: The limit of the function f(x) is obtained as L=limx→a-f(x)L'=limx→a+f(x) Then the limit of the…

Q: Consider the function G: R²\{0} → R defined by 12,8 (x10 + x10)² G(x): = Find an expression for the…

A:

Q: 7 - Let F(t) = cosnti" + sinntj* + 6tk* G(t)* = 2ti + t³j* %3D %3D Find a) lim[F.G*](t) t-3 b) lim[F…

A:

Q: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: Give an example of a function R→R that is discontinuous with the usual topology but is continuous…

A:

Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: calculate the limit of the function limT(æ → 0) [cosx/x2]]

A: To calculate the limit of the function.

Q: Prove that lim [x + ¡(2x + y)] = 1 + i using the definition of limits. z+1+i

A: Using the definition of limits we have to prove that: limz→1+ix+i2x+y=1+i.

Q: P) Find T(X) X→-1 f(x) -2 A) -1 C) 0 B) Does not exist D) -2 21

A:

Q: X- Zx +3x+2 lim

A: Solution of question as follows

Q: 2) Find lim f(x). X→1 f(x> X 2. 2.

A: here      limx→1- f(x)=1    and            limx→1+ f(x)=2 here                            limx→1-…

Q: lim f(x) = f(0). X-0

A: We have to prove that  limx→0+f(x)=f0

Q: Evaluate the limit lim 6 (²1) y→2_8y²(y − 1)³

A: To evaluate the following limit. limy→2 6y2-18y2y-13

Q: Evaluate the limit 9 1 - cos(t) 7. | lim t→0 t – 8 i + In(t + 8)j + -k t Enter your answer in i, j,…

A:

Q: Show directly from definitions that if f(r) and g(r) are real func- tions, bounded on (0.1), and so…

A: Here we have given that fx and gx are real functions, bounded on 0,1, so that limx→0+fx=2 and…

Q: Exercise 7. Evaluate lim vn(Vn+1- Vn). n00

A:

Q: (d) Consider the set [1, √5] C [−1, √10]. Explain f is not continuous by connectedness, compactness,…

A: Given: The function, f:-1,10→ℝ defined by, fx=x2,x>2x,x≤2 The set 1,5⊂-1,10. To explain: Why the…