Lim    4 - x2      x →2   x + 3 (b). Lim   4 - x2      x →2   x - 2 (c). Lim   1 + 8x + 6x3      x →∞    x³ + 7x² (d). Lim    x +6x3      x →0   4x + 7x²

Q: 2 -8 21. lim X3 3-x e2x-4 – 1 23. lim x+2 x2-4 25. lim X00 x2 +1 2.

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Q: x²-2x-3 lim a. (x-3)3 2-2r-3 x-3 (x-3)' x² - 2x-3 b. lim x² - 2x-3 lim 33 (x-3)3 c.

A: x→3+ limx2-2x-3(x-3)3=x→3+lim(x-3)(x+1)(x-3)3=x→3+limx+1(x-3)2=∞

Q: im ³√2x²-10 x-->3

A: Given : limx-->32x23-10 To find out limit we plug in 3 for x directly inside the cube root

Q: lim 4. 3- a2 - 6r + 9 5. lim 3+ a2 - 6r + 9 6. lim 3 a2-6x + 9

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Q: 2x- 14 | lim 7- x |2x – 14| lim %3D 7 - x x7+

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Q: 7. lim -3 x-9 x-9 (1+h)²-1² 8. lim h-0 h Final Answer: Final Answer: 9. lim -2r-15 (Зх-2)2- (х+2)2…

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

Q: (2+h)-8 lim h-0 x2-3x 5) lim X-3 x2-9

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Q: Lim x→∞  5x-3 − 4 / 2x-2 + 9 (ii) Lim x→∞ (x - 3)2 / x2/2 - 2x -3

A: Given limit   limx→∞ 5x-3-42x-2+9=limx→∞ 5x3-42x2+9=0-40+9=-49Therefore ,limx→∞ 5x3-42x-2+9=-49

Q: Lim             x^4 - 6x^2 - 8x-3/x^4 +2x^3 -2x-1                                              X…

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Q: 3. lim- 2x+ 4 3 X→- X-4 4. lim x→2 x2-6x+8

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Q: lim 7-4x-x4 2(x-2) lim 2x+1 人Y8 lim (Jx4-2x)

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Q: х —2 Га) lim x4-X-4 x- 3 (b) lim х+2 (х — 2)2

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Q: lim (2 - Vx +2)

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Q: lim X-4 (x²-3x-4)² X-4

A: We need to evaluate the following limit limx→4x2-3x-42x-4

Q: 3 lim WrZ_3K -x). x2-3X

A: The value of the limit is, - 3/2 The detailed solution is as follows below:

Q: 5x-3 – 4 (i) Lim- x-00 2x-2 + 9 (х - 3)2 (ii) Lim X-00 X4 2 7 2x – 3

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Q: lim (25-x2 X-D4 lim ( 3x -2) X-D3 lim (ax2 +4x+5) X-DO X+1

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Q: x2-4x+4 2. lim x-2 x2-x-2

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Q: a. lim (3x - 5) x->-1 b.lim x² -9 xxxx²²-4x+3 2 x²-9 c.lim XX x² - 4x +3 2

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Q: Lim x->4 (x2-3x-4)/ (x-4)

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Q: lim x->3 "x^2 - 3x - 10 / x^2 - 10x + 25"

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Q: lim -2 13-x-2

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Q: lim 3-V5+x 24 X-4

A: This is one of the simplest topics of algebra i.e. limits and this question can be done with just…

Q: x2 -x-6 2. lim -2 x2 -2

A: The given limit expression is limx→-2x2-x-6x2-2.

Q: /3x² – 3x + 1 lim 1– 2x x--00 V3 does not exist 3 2 -V3 ||

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Q: (а) 5x-3 – 4 (i) Lim x-00 2x-2 + 9 (х— 3)2 (ii) Lim X00 x2 7- 2x – 3 2 - 2х

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Q: lim x2 - 2x -15 / x2 -25 x->5

A: The given limits: limx→5x2-2x-15x2-25 Putting the limits, we have:…

Q: x² 4x + 5 lim 3x а. x+5 lim b. x+7 x² - 49 x - 7 lim С. x² - 3x + 2 2 - 4

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Q: Н.W: 3 lim x*-2x2-8 1-x2 х2-4 3- lim V3x-3 X-3 2- lim (1+x)2-1

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Q: 47. lim -4 3x-5x +7 8+2x-5x 2-2 48, lim 49. lim

A: we have to solve given problem;

Q: lim(-x² + x-2) x-2

A: Given,

Q: -3x + 4 a) lim x-2- x2 - 4 x2 b) lim x-3* x2 + 2x – 15 2x4 + 5x3 - 2х- 3 9x + 10 c) lim 5x7 + 2x6 –…

A: a) limx→2--3x+4x2-4=-3(2)+422-4=-6+44-4=-20=-∞limx→2--3x+4x2-4=-∞

Q: 8.) lim (-1+ x² – x³ + 3x*) 9.) x3-2x-1 lim x-3 co-X 2x2+3x+1 lim X+ 3x-5x+2 10.)

A:

Q: Evaluate

A: alimx→3−1x−3L.H.L x→3− means x approaching 3 from left ,x<3⇒x-3<0⇒limx→3−1x−3=1−0=−∞Or we can…

Q: lim x->4 (x-4/x2 -x-12)

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Q: lim X+0 2-√ 4-X² x ²

A: We can find the answer by finding the limit as below.

Q: (а) 5x-3 – 4 (i) Lim- x-00 2x-2 +9 (х— 3)2 (ii) Lim X-00 X T- 2x – 3

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Q: lim メ-2 ー×t6-× 2. 12-X X +6

A: Solving

Q: lim メ→-4 Vx+4 - 2

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Q: 1.) lim 3* x-2 2.) lim (2x+¹ -3) x-2

A: Given: 1.limx→23x2.limx→22x+1-3

Q: lim x>-3- x² +2xr-3 a. X- 7X b. lim x>-3+ x2 +2x-3 lim x>-3 x² +2x-3 C. X- ,X

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Q: lim *2+x-6. x²-4 2–4 is x-2

A: If we put the value of x as 2 in the given expression, The form will be 0/0 Because 0/0 is of…

Q: (х— 3)2 Lim 2 X→0 X 7-2х 2 (-3

A: To find limx→∞x-32x22-2x-3.

Q: 5x-3 – 4 (i) Lim: X-00 2x-2 + 9 (x – 3)2 (ii) Lim - 2x- 3 2

A: (i)

Q: im                           =x/x-2 x-> 2^+

A: Given limit is as below:

Q: lim(-3x² – 1) I-3 lim v3x2 - 6 X-2 (x-2)2 lim x-2 x2-4

A: Given that some limit problem and we solve this problem by using general property of limit.     Here…

Q: Find the following limits algebrically.

A: Part(a)

Q: lim(-x² + x-2) x-2 x+5x+4 lim x+2 2 +7x +6 lim I+3

A:

Q: 3x-2x 7. lim- X0 x2-x 8. lim x→∞ x²(ex – 1)

A:

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.