2 Problem 1: (a) State the definition of a limit, e.g., define what it means for limc f(x) = L (b) Provide an e-o proof of lim+1 x +3x = 4. If true nrovide a o ar falco

Q: 1. Use the e - ô definition of the limit to show the following: (a) lim(5x – 2) = 3 (b) lim VT = 0

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Q: ple: Find the limits for the follo 1. limx2(2- x) X-3 x2+4x+4 2.) lim Solutic

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Q: 5. Consider the limit: lim x² = 16. What is the largest allowable & that will "work" for e = 0.25 in…

A: Given  f(x) = x² To find : Value of delta using definition of limit

Q: 15. Evaluate the limit for the graph: lim f(x). *→2* 4 +∞o a. b. -1 14 A 2 -2 0 2 A C. d. 2 does not…

A: Solution:

Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: Evaluate the following limits 1-e²x)² 7x (a) lim- x-0 1-cosx (b) lim x² In 1 *** 1 9x²

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Suppose lim f(x) = 6 and lim g(x) = 3. x 4 x →4 Use limit laws to compute the following: f(x) + g(x)…

A: given  limx→4f(x)=6limx→4g(x)=3we know limx→a(f(x))n=(limx→af(x))n…

Q: dx Vx -9

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Q: lim f(x) = 2 lim g(x) = 3 %3D 4. Suppose that and then x→1 g(x) – 4 f (x) lim find the value of…

A: Given that: limx→1f(x)=2   and limx→1g(x)=3

Q: 1. Evaluate the following limits 5- cscx lim (xy)-(/2/2) 4cosy - (9/π)x

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Q: 1. Determine the infinite (oo or -o) limit as follows: x² - 2 (a) lim x2-x² - 3x + 2 sin x 1 x+ cos…

A: Topic = Limits

Q: 1. Use the e – d definition of the limit to show the following: - (a) lim(5x – 2) = 3 - (b) lim VI =…

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Q: 16. lim (2-3x) = −4 x → 2

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Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: 3. Evaluate the following limits. (a) 12 – 2x - 1 lim Va – 15 (b) lim (V17 - )(z - 5)13

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Use the e-8 definition of a limit to compute the value of the following limits: 1. lim -3x+1 3

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Q: (b). Compute each of the following limits. (i). lim,4 ". (ii). lim,0 tanz

A: For (i),     limx→ 4x2-x-12x2-4x=limx→ 4(x+3)(x-4)x(x-4)=limx→ 4x+3xPlug in the value x=4.=4+34=74

Q: Every limit as x → o can be expressed alternatively as a one-sided limit as t → 0*, where t = x-1.…

A: Given- limx→∞3x2-x2x2+5=limt→0+3-t2+5t2 To Prove- The above value of the limit using the quotient…

Q: se L'Hopital's Rule or otherwise to compute the following limit Lim -8x3 + 2x2 + 3x-1 x> 0.5 (2x –…

A: Explanation of the solution is given below...

Q: 3. Evaluate the following limits: +1 iv. lim 42 x-3 x+3 1 lim 4 v. 3 x2-2x-3,

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5. Evaluate the following limits. (a) lim (1+ e-2")3e²r+*. (b) lim (0.999999999)- In. |

A: 5(a) The given limit is: limx→∞1+e-2x3e2x+1 To evaluate the given limit.

Q: 2. Suppose DC R and functions f: D→ R and g: DR. Suppose to is an accumulation point of D and lim…

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Q: 2x - 6 Let f(x) = if x 5 -4x+ 20 Find the following limits: 1. lim f(x) = x-5 2. lim f(x) = x-0…

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Q: 3 n-∞0 2-ni (a) lim (b) lim Z-2 (c) lim 7-2 x²-4 x+4 4 x-2 I

A: Solving the first three subparts,