Using only the definition of limit, prove the following: 2n (a) lim 21 n→∞ = 0; (b) lim 1+ 1 + 2/1/2 = 1. n→∞

Q: Evaluate the limit 49 – t - lim t- 49 7 - t

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Q: Use the formal definition of limit ( ε-δ-definition) to show that lim x -> 2 for (5x-3) =7

A: ε-δ-definition of limit : For every ε>0 there exists a δ>0 such that  whenever or

Q: tanh x lim r+0+ sechx- 1

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Q: if a -6 Calculate the following limits. If the limit doesn't exist but it makes sense to call it o∞…

A: given that                                 we have to find value of limit as well as value of…

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

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Q: Evaluate the limit assuming that lim g(x) = -8: x-2 lim g(x) %3D x-2 x2

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Q: Evaluate the following limits. If necessary, enter INF for ∞o and -INF for -∞. a) lim In (7x7 +5) =…

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Q: i. Using Arithmetic of Limits, find limn→∞ 3n / (5n + 3)  ii. Working directly from the definition…

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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: 1.) Calculate the limit: lim(2x² – 6x +1)

A: We have to find the limit of the function: limx→22x2-6x+1 Since this is determinate limit so we just…

Q: Use the definition of limit to prove lim {x -> 5} = 2x-3=7

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Q: Using the precise definition of a limit, à in terms of & for lim (2-3x) = -4 is E/-3 X-2 A) True B…

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Q: 1. (4 points) Use an algebraic technique to evaluate the following limit. lim ( ) 1 2 tan r- tan x-1

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Q: 1. Evaluate the following limit: x? -4 a. lim- 1+2x + 2x – 8 (x²-9) 2 b. lim 1+3 (x -3) (t - 3) c.…

A: If putting the value of variable value of function approaches 0/0 we should apply L hospital rule…

Q: Use the Basic Limit Laws to evaluate:

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Q: Prove lim x³ = X→3 27 using the 8, & definition of limits.

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Q: lim (x³ + 4x² + 4x – 1) = -1, a-2 1 lim - = 1.

A: Given,

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

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Q: lim -2)2 x-2 x2-4 3.)

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Q: Use the formal definition of limit ( ε-δ-definition) to show that lim x -> -1 for ( (x4+x+1) / x3 )…

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Q: Evaluate the limit, using L’Hôpital’s Rule if necessary

A: Given: limx→∞x2+4x+7x-6

Q: 3) Suppose that the limit of f(x) exists at z = 1 and let lim f(x) = 5. Find the following limits…

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