(6,5). (1.4) (-4,2), (6,2) -2 6. 8 -2 9(1-2) lim f(z) = I4-4- -4 00 4.

Q: Give precise definitions of the following statements.

A:

Q: 1. Simplify: yl1 1 x1?y,20 2. Identify the vertex of the parabola y = x + 4x + 3. (-2, -1) (-2, 3) O…

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Q: (2 -1) s lim z

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

A:

Q: х2 +x — 2 Vx + 4 – 2 - - (а) lim x→-2 (b) lim x + 2 y y 2 1.00 1 0.75 0.50 -3 -2 - 1 1 2 3 -3 -4 -3…

A: (a)limx→-2x2+x-2x+2blimx→0x+4-2x

Q: Q3) Find: (1) lim, 1+cos 2x (2) limx→-2- (x + 2) |4-x²| 2-x

A: Q3)1Here, we need to calculate the limit of ,limx→π21+cos2x4x-π2

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A: Given ,limx→5x2+13x+40x+5

Q: t2+3t+2 2. lim t--1 t2-t-2

A: To find the limit of the given function

Q: -7; x<-3 { (x + 2)3 – 6; (x- 2)2 – 5; f (x) = -3 < x < 0 %3D x 2 0 1. lim f(x) = X→-3+ 2. lim f(x)…

A: Given: f(x) :  -7  ;  x ≤ -3 (x+2)3 - 6 ;  -3 &lt; x &lt; 0 ( x -2)2 - 5 ;  x ≥ 0

Q: x--2xy lim (x,y) - (2,1) x²-4y² .A 3 .B 1 4 .C .D 1 2 ONIM

A:

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: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: 1. lim (y – 2y+7) 2. lim (y² +5y–1) y→3 y2 3w - 4w+2 3. lim 3w – 2w+7 w² +1 | 4. lim w2 w -5 w-1

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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: Prove the limit statements

A: Given: fx=4-2x,x&lt;16x-4,x≥1 we know that limit of any given function at given point exist only if…

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: 2.7h - 1 lim 2.8h 1 lim - and - h 0 h h

A: To see explaintaton

Q: x2 – 4, x 3 -

A:

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-

A:

Q: 1 Find lim 3 s-2- \s-2 s²–4,

A: Given, Evaluate lims→2-1s-2-3s2-4

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: z² + 4z + 4 f(2) = - 4z +4 f(2) =미 lim f(2) = 1. Z-12

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 2 points f(4+h)-f(4) If f(x) = ax + 8Vx and limh-0 = 5, %3D 3h then a= 13 O 17 O 12

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Q: 10z+ -1 f lim r+7=- 5, then - (A) m=3 and b-2 (B) m= 2 and b 3 (C) m- 3 and b- 10 (D) m=4 and b-2…

A:

Q: (4+ 43) (x + 43) -(16 + 43)x limy→ -43 limx. x + 43

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Q: 2- -1- -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 3 -1 -2 -3 --4 -5 -6 -7- Provide your answer below: lim f(x)…

A:

Q: . What is lim tan(x)? Why? 2 AY 10 8 6 4 2 -1A -0.5 0.5T, 1.57 27 2.57, 37 -4 -6

A: 1) limx→π2+tan(x)=? 2) limx→0+f(x) =? and limx→0-f(x) =?

Q: lim f(T) = 1, lim f(r) = – 00, I -2 f(-2) = %3D 4- 3- -5 -4 -3 -2 A1 2 3 4 -2 -3- -4-

A:

Q: -2 0 1| 3 What is the 6 5 4 3 2 1 0 -1 -2 -6 lim f(x) for the following graph? X→-3 -5 -4 -3 -2 -1 0…

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Q: 1 1 dz = lim V3(w + h) – 2 V3w – 2 h 1- dw h-0

A:

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

A:

Q: Find the limit.

A: We have to find the given limit

Q: 8- 6- y = h(x) y = h(x) -4 -3 2 -2- 2. lim, h(x): 3. lim,→2- h(x): 4. lim,-2+ h(x): 5. limy-2 h(x):…

A: Find the following value from the graph:

Q: f(x)= -5 - x^2 A) (f(8)-f(4)) / 8-4 B) (f(4+h) - f(4)) / h C) lim h---> 0 (f(4+h) - f(4))…

A: f(x)= -5 - x^2  Find A) (f(8)-f(4)) / 8-4 B) (f(4+h) - f(4)) / h C) lim h---&gt; 0 (f(4+h) - f(4)) /…

Q: -11x lim I+00 11 + 2x -1 6x – 12 lim 1-00 r3 + 9x – 14 ,2 lim x→0 12 – 15x? V2² + 15x lim 5х — 13…

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

A:

Q: -7 -1 3 5 -1 -2 -3 -4 ー5 -6- -7 -8- de your answer below: a. lim f(x) = xラ-6 5. lim f(x)= O

A: Given:   Graph is given

Q: 19. lim x→2- x² – 4 eas y + 6 21. lim y→6+ y2 – 36 -

A: Given that limx→2- xx2-4 limx→6+y+6y2-36

Q: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

A:

Q: 7 B lim f (x)% = 6 T--2- A 2 1(-0.1, 0.5) B2 -7 -6 -5 -3 +2 2 -1 -2 -3 F E 3.

A:

Q: 1 2 1 + lim Р-(-1,2,0) х- 2 у -5 z+4 II

A:

Q: 1 4. lim 2t-1 t-

A: Note:- We will answer the 4th question since we answer only one question at a time. Please submit a…

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

A:

Q: 2cosh(z) – z – z² lim z4

A: We have to calculate : limz→02 cosh…

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

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Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

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