7 Exercise 5: Calculate the following limits, using the 6-e definition of a limit (i.e., provide an e-8 proof for the following limits) (a) lim |1 - 3x| () +2 (b) lim 2 - 5x ft auU : Pd (c) lim r3 Ix 2 (d) lim f(x) where (h Ahoe)* f (x) = H 3 ,2 x < 3 7, 2x3, x >3 x 3 dalw boowloong u t

Q: 5. Evaluate each expression using the given graph of f(x). lim f(x) a) x-1- 2- 1- b) lim f(x) -2 -1…

A: Given graph, The objective is to find,  a) limx→1-f(x)  b) limx→1+f(x)  c) limx→1f(x) d) f1 e)…

Q: Use the graph to evaluate the limit. 1) lim f(x) X-0 N -1 -1+ A) does not exist 3 4 x B) 0 C) 2 D)…

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Q: Calculate the following limits. t2 - 2t - 3 lim t43 (t-3)3 a) |x-5| b) lim x+5- x2-4x -5

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Q: Evaluate the following limits when they exists: x+x3x²+1 (a) (5 points) lim→>-1 x+1

A: To evaluate the limit limx→−1​x+1x4+x3−x2+1​, we first check if direct substitution leads to an…

Q: 4. Evaluate the following limits (3+ 1)? -9 (a) lim, 40 (b) lim, -1

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Q: Find the limit: lim Vx -4 x- 16 x - 16

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

Q: Exercise 1: Provide an e-6 proof for the following limits (a) lim 33x21 r+3 (b) lim 2-1|

A: To establish the limits of the function using epsilon -delta definition

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Find the limit algebraically. lim 46) X-2 (x3 + 5x2 - 7x + 1) 5 x

A: To find a limit algebraically we just plug in the value x approaches in the expression the limit has…

Q: Evaluate the limits algebraically (using limit laws): Vt2 + 9 – 3 lim- t-0 х2 — 1 lim(2x² – 3x + 4),…

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Q: 3. Evaluate the following limits, if they exist: 1 (a) lim 1 +3 2x x→-0

A: