b) Evaluate the following limits: 2(-3+h)2 18 i. lim h→0 - h (t-V(3t+4) ii. lim t→4 4-t -2X 6e4x – e-2 iii. lim h→0 8e4x -e2x +3e¬x 699

Q: Vx² + 12 – 4 33. lim x-2 x-2

A: Explanation of the answer is as follows

Q: (a) lim 5x*+3x²-6r+10 2x4-3.x-4 4. Find the limit:

A: Given, Evaluate limit :limx→∞ 5x4+3x2-6x+102x4-3x-4

Q: 1 (a²- a→1 (a²-4a+3)3 (а?+4а-5)2 4. Evaluate: lim

A:

Q: 5x + 2lnx 8. lim X+3Inx

A:

Q: 2 lim y² - 7y + 12 3 y → 4 y - 64 1 48.

A:

Q: 3 4x 7 lim x00 7x2+8

A:

Q: 2. Find lim (√x + 2 = √2).

A:

Q: 28x2 + 949x – 2124 а. lim x→-36 37x² + 1380x + 1728

A:

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: Evaluate:

A: We can find the limit of an expression by applying the limit point as the value of the variable in…

Q: x2 - 9 lim X-3 x→3 V – 4 x2+7

A:

Q: Зх + 5 3 lim V 6х — 8

A:

Q: 7x² +6 9. Lim x→ too 3xr – 7 土0

A: We have to evaluate given limit.

Q: 9x2 lim x+00 x+2

A:

Q: x3+27 b. lim x--3 x+3 hint: a3 + b3 = (a + b) (a2 – ab + b2)

A:

Q: +1 limx0 t2+1

A:

Q: For * + 3. lim (02)-(0,0) :? O A. -2 В. 2 C. Does not exist. D. 0

A:

Q: V9x2 + 4 96, lim x-0 6x +1 X00

A: Solve the limit

Q: 2. Describe how to deal with the singularity in the integral if one wants to evaluate this integral…

A: Given integral is  ∫01x-12e-x2dx           (i) Let fx=x-12e-x2 Clearly, x=0 is a singular point of…

Q: (a) Show that x* is a global minimizer of g x* Pg= { € R" :x= =prox (x)}.

A: To show that: is a global minimizer of

Q: 5æ²+8 The limx→t∞ 13x²+8x 13 13 13 5 Clear my choice

A:

Q: 2x – -12x + 40 3x2 + x – 14 14) lím エ→2

A: We will find the value of the limit as following.

Q: poge( a). liun +3x=12X+4 x4X

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

Q: Q 7 Find lim y+21y2 +71y + 51 y2-9

A: Consider the given limits

Q: 0.Lim ュー)×40,2 メ-2 メ→o “波 (1+x) - 1 4)Lim *キX メーフ。

A: In this question , we can find the limit .

Q: V5x+4-3 3) lim X-1 x-1

A:

Q: 2. Find_lim (3x³ + √9x6 − 2x³ ) ∞-1x 2

A:

Q: Find the limits 3x lim x→-5 2x + 10

A: Our Aim is to find the limit of the expression given below:-limx→-5- 3x2x+10-(i)

Q: de 4 V4x* +3 lim 5x +4

A: Divide the Numerator and denominator of the given expression by x2

Q: B: Find: Vx+4-2 limx0 lim,-

A: Given, limx→0x+4-2x we have to find the limit.

Q: 312+ t 17. lim .3 t-4t + 1

A: Given,limt→-∞ 3t2+tt3-4t +1Here denominator has degree 3 and numerator has degree 2.Thus,…

Q: lim 3x+9x2-4x+17 5x3-3x-14 004-2

A: limx→∞3x3+9x2-4x+175x3-3x-14

Q: 20x2 – 3x Calculate lim x→0 ° 3x5 – 4x2 +5

A: It is given that, limx→∞20x2-3x3x5-4x2+5.

Q: 2x2+11x+5 #5) lim x3+125

A: Solve for limit

Q: lim m 42 -1 t² +1-2 ܐܝ: (b

A:

Q: Evaluate lim (r + 2x° - 5}.

A: Limit is the value that function approached if input approaches to some value. It has many…

Q: x2-2x4メ4x Lim (X-1)²+ y2 2 2 .

A: Solve using  properties of the limits