2x-1: x>1 29. f(x)=-1: x=1 1-4x; x<1 Evaluate a. lim f (x). b. lim f (x), and c. lim f(x). 27, 7,

Q: (х-а) 2. lim Vx-Va X→a

A:

Q: Give precise definitions of the following statements.

A:

Q: Vx + 2 – 2 Evaluate the limit lim x→2 x2 – 4

A: We can evaluate the limit in the following steps.

Q: x-1 numerically. Vx-1 Estimate lim

A: Using rationalization method.

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: с — 2 а. x→0 x5 – 43 х — 2 lim- b. lim x→2 x5 - 4x3 х — 2 С. lim x→-2 x5 4x3

A: a) limx→0x-2x5-4x3 Left Hand limit- The function decreases without bound. so, limx→0-x-2x5-4x3=-∞

Q: x-7 Evaluate lim- +1 Jx-3 - 2 Vx- 3 –

A: Consider the given fraction: limx→7x−7x−3−2Rationalize the…

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: 1-y+2,7-2,5 Q6) find the limit lim (xy)-(00)

A:

Q: V5x + 36 – 6 Evaluate the limit: lim x →0

A:

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

A:

Q: 2z-i Our aim is to prove that lim = 2. Which among the following options is true? Zco z+1

A:

Q: (a) Evaluate limits x? - 3х - 4 i. lim- X4 Vх - 2 3x +1 lim i. x--* J4x -1 X-0

A:

Q: V5x + 36 6 Evaluate the limit: lim x →0

A:

Q: x + 2x-35 Evaluate the limit: lim エ>5 2x + 10

A:

Q: (x²+5x – 6 Evaluate: lim x-1 А) 5 B limit does not exist (c) 3 D) 7

A:

Q: x² - 7x y +12y Evaluate lim(x,y)→(3,1) х- Зу

A: The given expression is limx,y→3,1x2-7xy+12y2x-3y

Q: 3 – x| Find the limit lim x→3 x² – 9

A:

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: Ans Find the limits. 2x +x- 1 = -3. 1. lim x +1 X-I

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (a) lim n-0 2 – ni x² – 4 (b) lim x + 4 x² – 4 (c) lim x – 2

A:

Q: f(x)= (x^2-2 where, x/=4). Calculate: lim x-4^- f(x)

A:

Q: x2 – 4, x 3 -

A:

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: 6 lim | 3 x² – 32 X+3 X - Enter I for oo, -I for -00, and DNE if the limit does not exist. Limit =

A: We shall find left hand limit first if it doesn't exist then limit not exist, if exist and finite…

Q: Vx? +8 – 3 | Evaluate the limit: lim x→-1 x+1

A: Given:  Let y=limx→-1 x2+8-3x+1 To Find: To evaluate the given limit.

Q: (x² – 2, x 0, x→0*

A: Given, fx=x2-2,    x&lt;02-x2,    x≥0

Q: 3* –1 lim V1+x -1,

A:

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: |3 – x| Find the limit lim x→3 x2 – 9

A: For limit to be exist, Left hand limit must be equal to Right hand limit.

Q: f(x) – 5 = 3, find lim f(x). 81. a. If lim x→2 x – 2 x→2 f(x) – 5 b. If lim x→2 x - 2 = 4, find lim…

A:

Q: Find the value (1) lim (x,y)-(2-3) (3) lim (xy)-(11) √x-√√y of the following limits: x²-2xy + y²…

A: As per the instruction, post the question again for question (5). For (1),    limx, y→2,…

Q: 13. lim f(x), where Sx+2 xS2 3x-5 x> 2 f(x) = 14. lim f(x), where Sx* - x +1 x 3

A:

Q: 5x b) lim lim-0 2ln(x+1) ex-e-x c) lim lim-0 2x x2-2x-3 d) lim lim-3 x-5x+6

A:

Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: - [x² + 2 if x < 2 (x) l(x - 3)2 if x 2 2 (a) Find the following limits. (If an answer does not…

A: Given function:

Q: Find the limits. (x) = 2x² – 3x + 4, g(x) = Vx + 2 (a) lim f(x) x-2 (b) lim g(x) = %3D

A:

Q: xample: Using the Sandwich theorem 1. If V5- 2x2 <f(x)< v5– x² for -1< x< 1, find lim f (x)

A:

Q: {x² +7, 14, x = 4 lim f(x), where f(x) =

A:

Q: x² +1 Evaluate the limit of limx ( - ax – b) = 0 - x+1

A:

Q: 5) lim f(x) x--2

A:

Q: 23 - Vx - 47 Find lim x+ 24 X→-24

A:

Q: lim Q3/ Evaluate -costx) 3 sec x (1+ X /2

A:

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: 3 - m3 x + 2 2 . lim lim x-2 x + 2'x2 – x – 6 A- m4 lim as x approaches m 1. LO

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 9 – y². |-(16 * 10)x – (4 * 10) lim . -] + lim y--33 + y x + 10 x--10

A: Given,            limy→-39 - y23 + y + limx→-10-16*10x-4*10x + 10

Q: x' -x+1 Evaluate (iii) lim 5x' +7 and show work

A: The given limit can be evaluated by taking x3 as common from numerator and denominator

Q: Along the path x = e" find y +4xy lim (х.)- (1,0) Зх — у -3 does not exist O -2 -3 2 0 30

A: Explanation of the answer is as follows

Q: limx--1f(x) Let f(x) = (x² – 1)/C(x| – 1)

A: