(2x 1, ifx <-2 if x 2-2 %3D 5. lim X-2 (x + 3, .3

Q: 4. lim xy (xy)-(0.0) v2-e-1

A: To evaluate limx,y→0,0xy2-exy-1 Substitute t=xy, then as x,y tends to 0,0 implies t tends to 0.…

Q: 2h 4. lim h0 2h S(x) dr

A: Answer and explanation is given below

Q: arctan(kx) e2x – 1 lim \k=1

A:

Q: 4 ex lim X 4 + 3e*

A: Given,              limx→∞4-ex4+3ex

Q: arctan(kx) e2x – 1 lim k=1

A: To evaluate, limx→0∑k=18arctankxe2x-1 Then, the above expression can be re-written as,…

Q: Зх-7 (1) lim x--o V4x2+x-11

A: Explanation and solutions is given below....

Q: X x+cos (-3x) 16) lim

A: To find the limit  limx→-∞xcos-3x

Q: Find the limit

A:

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: for e5x – x³ x 0 (i) lim h(x) (ii) lim h(x) (iii) x→0- x→0+ lim h(x)

A:

Q: - 2 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X&lt;0. Therefore, Sin(x)&lt;0. Therefore, the…

Q: 2x2 – x – 3 (d) lim x→-1 x² + 5x + 4 2x – 8 (e) lim r→4 x2 – 8x + 16 x2 (f) lim r--2 2x + 4

A:

Q: e7x + e-7x _ 2 lim x → 0 5 x2

A: Evaluate the given limit as follows. limx→0e7x+e-7x-25x2=e70+e-70-2502=1+1-20=00 Since 00 is an…

Q: c. lim In³ x

A:

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: 4x +4 lim (2,y) (-1,2)` x² + 3xy – 3y2 + 3xy - 3y2

A:

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: RNEK : lim X-0 - dt = ? 14 + 1

A:

Q: 4x e lim x→0 r2

A: The series expansion of ex is ex=1+x1!+x22!+x33!+x44!+...

Q: 1 1 V13+x 3 h. lim X→0 X + 4

A:

Q: d. lim h(x) Preview e. lim h(x) = x→00 Preview f. lim h(x) = 00--x

A:

Q: 1. lim Vx? – 4 x→2+ – 4 2. lim /x(5 — х) x-5 4x 3. lim x-4+Vx-4 E.2

A: We have to find

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

A:

Q: ху — 2х — у +2 lim (K. y)-(1,2) X* + y² – 2x – 4y + 5

A: Let  S  be an open set containing  (x0,y0) , and let  f  be a function of two variables defined on…

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: 3x-7 lim zー8 Sx +1

A: limx→∞3x-75x+1

Q: x°+4 lim 4 x+ 0x"+5 ||

A:

Q: (c) lim 1 In x x→0+

A: To find out the limit

Q: |x² +1 if x 0 x→0

A:

Q: x2 – x – 12 lim 2. Evaluat" t→4 3x – V16 – x

A: Limit is the value of the expression as the independent variable approaches certain value, not…

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…

A:

Q: 1x+21 Ex.2: lim ダー→ -2 (x+3) x+2

A: limx→-2-(x+3)|x+2|x+2

Q: x° – 27 lim %3D x-3 D - 27 O 18 O27

A: The given expression is limx→3x3-27x-3.

Q: b. lim -3 where c is some fixed real number. +x+c-2 x>e

A:

Q: 4. 21. lim 2+ Vx

A:

Q: 1. lim f(x) where flx) = (-3x + 8 if x -2

A: Use limit condition.

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: b. lim X-0* e -3/x 2 X²

A: Please see the attachment

Q: 1 lim x-0 X 1 ´dt x4 1 = ? 3x2

A:

Q: х — 1 If y = lim x→0 Vx + 3 – 2 The value of y = 4. %|

A: Given:

Q: ni eoulav sd no 2x + 5 13. lim x→-2+\x + 1八 +x ber

A:

Q: 2x (1) lim x→0 3– vx+ 9 -

A:

Q: 1 – sec(2x) 6. lim x→0

A: Topic:- limit calculation

Q: b-4+ Jb 3x(x – 4) Answer "True" or "False" for the following: In(x – 1) Ji 3x(x – 4) In(x – 1) |…

A:

Q: 1/x 2 In(5x) H lim 2 5x = lim lim lim X- V 5x 5x 2 5x

A: The solution of given problem as follows:

Q: х — 1 lim x→1+ Vx + 2

A: Here we need to find the right hand limit only.To find the required limit substitute the variable…

Q: 1 lim(2x + 1)zx =? X→0

A: In the given question, the concept of Limit is applied. Limit The limit formula is employed to…

Q: 3 lim h→0 3h + + 1

A: Here we have to evaluate limh→033h+1+1