Ex x-2 XE3, X-2 12) Consider メレ3 2) lim. (f(x) b) lim. (f(x)

Q: (х-а) 2. lim Vx-Va X→a

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Q: Give precise definitions of the following statements.

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Q: If x- 2 1 lim -2 f(x) – f(2) then, the slope of the tangent line at the point (2, f(2)) is m =7. %3D…

A: By limit defination of f'(x) at point x= a

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

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Q: 2. 2xy lim (x.y)-(0,0) x² + 2y6

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Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

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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: IF FLX)= and Lim F(X)6 F(-)=2 b X<l Find a,b when X#0

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Q: 2. f(2)-1(;) If f(x) = arcsin x, then lim is X- 2

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Q: If (x, y)lim(2, 3) f(x, y) = 4, can you conclude anything about f(2, 3)? Explain.

A: Assume the function z = f(x,y).First observe the value of the limit for x followed by y.

Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

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Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

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Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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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

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Q: 2) fle -2x 22 アー4nt6 6) lim F(x)=2 c) limfe) Xー→2t こ doesn't exist a) lim f) = 2 %3D Xーラ -2

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Q: Use the graph in Figure to find each of the following:

A: Limit L of a function at x=a is the value that a function approaches from both the left hand side…

Q: What is lim tan(x)? Why? AY 10 8 6. 4 2 -0.S 0.ST, 0.5n, 1.5a, 27 2.5m -4 -10

A: Given limit is limx→π2+tan(x) As shown in the graph of tan(x), as x approaches π2 from right side ,…

Q: пу-1 lim y→0_2y² y(e2™y–1)

A: To evaluate limy→0(πy(e2πy−1)+πy−12y2) Rewrite the given expression:…

Q: 3. y = f(x) 4 6. -1 lim f(x) =

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Q: Let h(x)

A: hx=x2,      x&lt;23,       x=22,       x&gt;2 Now, The left hand limit at x=2 is,…

Q: if f(5) = 4, f'(5) = 7, then lim of (f(x²+1) -4)/(x²-4) = ?? when x goes to 2

A: Please see the answer below.

Q: x2 – 4, x 3 -

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Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

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Q: Find : lim x*-4y2 if it exists. а. (x,y)→(0,0) x²+2y2 x²y+xy² b. lim if it exists. (х,у)-(2,-1)…

A: Given To check it is exist or not  If it exists then find the value

Q: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x&lt;2x3-1      if x&gt;217           if x=2  To find…

Q: 2-y lim 7+ 6y² y-

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Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

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Q: tan X AWO Lim メーラク メ O Lim 2, 5+s° (3) Lim J-→の y生チンチアメチタ

A: Since you have posted multiple question in this question so I have solved first three question…

Q: y of -4 -2 -2 (a) (1) (b) lim f(x) x-1 2.

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Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

A: E

Q: 2. メー gu)= - fex) = X üls Is1 3メ-1 احب lim (fog) x メー

A: We have to find limit

Q: 1 4. Find limx→0+ ( ) ex-1

A: Given :          limx→0+1ex-1-1x

Q: Vx? +12 - 4 x²-5x +6 2x-5x +6 a- Lim cos x b- Lim c- Lim d- Lim x - 2 x'-8 3x -8 --

A: If in limit denominator and numerator forms 0 by 0 use L hospital rule

Q: *+xVア-2) lim )(4,16) x - Vy

A: Here we have lim(x,y)→(4,16)x2+xy-2yx-y

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

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Q: Find the limit.

A: We have to find the given limit

Q: 7- x2 if x 2 Iff (x) find lim f (x). I→-1+ |

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

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Q: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

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Q: 4 6.xy1 Find lim if it exists. (x,y)→(0,0) x² + y8 *

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Q: tan(ху) = ? .2. (х,у) >(0,1) х*y+x lim

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Q: Given fx) ={ax + b (2x – 6 if xs -2 if - 2<x < 2 if 2 sx 2. Find the values of a and h such that lim…

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Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

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: 4f(x) + 2x – 14 Suppose that lim z+1 5. Find lim f(x). I→1

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