Exercises (1.6): (1) lim vx (2) lim(sgn(x2-1) + sgn(x? +1)) X-0+ (2x +1, x2 2 (3) lim f(x), limf (x) and lim f(x) if f(x) = %3D エ→5 X-2 (x+3, x<2 -2x, (4) lim(x| + sgn(x)) (5) lim f(x) if f (x) = X+2 x²-4x +1, x> 2

Q: 20. lim_ v3 – x x→3-

A: We have to find the limit

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: Find the constant a such that Va ax +4-2 lim

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: (b) Show that if lim sn = +o∞ and lim tm > -x, then lim($n + tn) = +0.

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Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: -xy lim (x,y)→(0,0) x²+y2

A:

Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: 1-coskx 2. lim kx = 0.

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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: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) S-x+7…

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Q: 8. e 1 Build a table to estimate lim x+0 X

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Q: Find the limit. lim x+v-1 (x, y)- Vx+y-1

A: The given limit is of 0/0 form. In this type of limit problems, we try to remove 0 from the…

Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: 2. Find the limit or show that it does not exist: lim (2,y)→(0,0) 2x6 + y?

A: We have to find limit

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

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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: 9. Build a table to estimate lim sin - (Hint: Use multiples of T) (x³ - 3x2 + 6– 2x) 10. Use a table…

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Q: 4 Find lim х — 4 Væ – 2 x→4

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Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

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Q: 2x lim(x,y)→(0,0) x² + x + y²

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Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

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

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

A:

Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

A: Explanation of the solution is given below...

Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: 3* –1 lim V1+x -1,

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 5. lim V2x +1 X-4 6. lim -) ズー1 x-1 CABA 3x+4 if x <-3 AT 7. lim f(x), where f(x) = 2-4 ifx2-3

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Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

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Q: 1 lim sinx x2 x→0

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Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

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

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Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

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Q: V2x(x-1) 3. lim-1 Jx-1|

A: Given limit, limx→12xx-1x-1

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: Determine lim In/xy. (x,y)(e4)

A: lim(x,y)-&gt;(e2,4)lnxy

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: alignment at x² + x – 1 limx→ 2x2 — х + 1 has a horizontal at???

A: Topic = Limits

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: II- Calculer les limites suivantes: CS Scanned with Camx³x3+4x-5 0071-x II- Calculate the following…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.