1) Find the limit as x approaches 2 from the left and from the right (if they exist). Does the limit exists at x = 2? [x² – x + 2, x <2 f(x) = 5, |2-x?, х>2 x=2

Q: 2) Evaluate the limit at x=1 for: x* + 7x2 – x – 2 f(x) x² – 5x + 4

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Q: The value of the limit 3 lim (1- z/2 is equal to O e-3/2 O e3/2 O e2/3 O 1 The limit does not exist

A: Given: The limit limz→∞1-3zz2.

Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

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Q: 4. Does f(x) = : (0, 00) → R have a right limit at x = 0? If yes, compute the limit. If not, explain…

A: We need to calculate when x-&gt;o+ from right side then f(x) exist or not.

Q: Let f(x) = 4x² + 6x + 2. According to the definition, f'(x) lim h→0 (Enter the limit in reduced…

A: Given f(x)=4x2+6x+2

Q: 1 Discuss the existence of the limit lim x 0 x2"

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Q: In finding the limit for  (x)2/x as x→+∞ by L'Hospital rule, which limit should appear in the late…

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Q: 3. Can f (x) approach a limit as x → c if f(c) is undefined? If so,

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Q: Is there a real number a such that 3r + ar + a+3 lim --2 r+x + 2 exists? If so, find the value of a…

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Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: Compute the limit as x approaches infinity of x^e-x

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Q: If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist…

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Q: What is the limit of f(x) = 3 as x approaches π? (If an answer does not exist, enter DNE.)

A: Given:

Q: 1 Q.3: Discuss the limit of f (x) : at x = 0", 0*,-∞,+∞, with graphs.

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Q: Let            fn(x) = nx/1 + nx2  (a) Find the pointwise limit of (fn) for all x ∈ (0,∞).

A: Given : fn(x)=nx1+nx2; To find the point wise limit of this function for given values of x: We have…

Q: Find the limit as t-➜0 of r(t)=

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Q: Find all values of c such that the limit exists.

A: Our Aim is to find the value of c from the given expression such thatthe limit…

Q: 6 Use the e - d definition of a limit to prove e lim 1+2 r2 + 2 1.

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Q: When proving the limit lim(x² + 4x - 1) = 11, and e > 0 is given, what is an appropriate choice for…

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Q: Find the limit of f (x) = √(14 + √x), defined on X = [1, ∞)

A: The given function is: f(x)=14+x  is defined on [1,∞).

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

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Q: Find a value of the constant k such that the indicated limit exists. 8 -5 lim x-0 ekx +5

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Q: 1. Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 - x im x² – 4 sin 2x…

A: Find the limit of the given function  1) (2-x)/(x2-4) , when x tends to 2 .  2) sin(2x)/sin(3x) ,…

Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: 1 Let f(x) According to the definition, 7 4x f'(x) = lim h0 (Enter the limit in reduced form) %3D

A: Givenf(x)=14x-7

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: Find a value of the constant k such that the limit exists.

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Q: 2) Suppose that the limit of a function f(x) exists at z = a. If lim f(x) = M and lim f(x) = N, what…

A: Given:- f(x) exists at x=a We have to find the relation between M and N for given limit of a…

Q: Let ƒ(x) = (3x - 1)/x. Make tables of values of ƒ at values of x that approach c = 0 from above and…

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Q: If the limit of f(x) as x approaches cis 0, then there must exist a number k such that f(k) < 0.001.…

A: Explanation: If limx→cf(x)=0, the for any positive ∈, (Like 0.001) there is a positive δ such that…

Q: Find the limit (if it exists) of Anx1 as n approaches infinity, where

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Q: 9. Determine the exact answer for the following limit analytically: Vx+1-2 lim- x-3

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Q: Given that g(x) = 2ª + 2 is continuous on its entire domain, find the limit of the g(x) as x…

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Q: find the limit as x approaches to infinity (x-3 / x+1)^x/a

A: We need to evaluate the value of the following limit limx→∞x-3x+1xa Formula Used:  limx→∞1+mxx = em…

Q: - Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x)) c-2-VX-+4 /sin'x x>1 x>0 d- lim x+1…

A: Limit values

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

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Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: 3 Evaluate the limit lim [(2-1)(3– 2i)+1–3i] and use the definition of the limit (e-6) z-2+i to…

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Q: Find the maximum value of 8 > 0 that satisfies the limit claim corresponding to ɛ = 0.1, that is,…

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Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

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Q: What result do you obtain when you evaluate the limit (RHL and LHL) of the limit of (x^2-16)/(x-4)…

A: Given f(x)=x2-16x-4 LHL=limx→4-f(x) and RHL=limx→4+f(x) Here if LHL = RHL, then limit exists.

Q: Find the limit as h approaches zero of f(x)=[1/(x+h)^2-1/x^2]/h

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Q: Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2     (m not =0)

A: Consider

Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: Find the limit. lim (e 4/x+ 9x) x/2 x-0 0 1 00 e2

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Q: 3. Compute the limit algebraically Vx + 3x2 lim 6x 1

A: Solution: The objective is to find the limit of the given function

Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: if r =-1 A if z + -1 2. Is f(r) = continuous at r =-1? (Show your work using limits.)

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