Using the ε - 8 language to prove: lim √√√√c, for any c≥ 0. x c =

Q: -1 Evaluate: lim X+0

A:

Q: -e g). lim [In(6x² + 5) – In(3x² – 6)] h). lim ズ→の

A: g) limx→∞ln6x2+5-ln3x2-6h) limx→-∞e2x-e-2xe2x+e-2x

Q: lim xln(x+2) x →0+

A:

Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

A: We have given a limit function;

Q: Evaluate lim x + Væ² - x" + 2x

A:

Q: Lim X-o413-xl-1 76-JC

A: Evaluate the limit.      limx→416-x23-x-1

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: √√5 - 2x² ≤ f(x) ≤ √√5 − x² - for −1 ≤ x ≤ 1, find 63. If √5 lim f(x). 0-x

A: We are given two functions that bound f(x):5-2x2≤f(x)≤5-x2for x in the range -1 to 1.

Q: Use numerical evidence to evaluate lim (5. (5. √x + 4) x18 f(x) X 1 100 10000 1000000 Type in oo for…

A: By using numerical evidence to evaluate the following limit. limx→∞5·x+4

Q: x2 – 3x – 10 lim x+5 x2 – 10x + 25

A:

Q: Evaluate using the identity: a3 − b3 = (a − b)(a2 + ab + b2)

A: Given, limx→1x4-1x3-1. The objective is to evaluate the limit.   Apply the identity: x2-y2=x+yx-y…

Q: ) lim (Vx+3 +Vx) 14

A:

Q: 5x - 1 b) lim Z-+0+ 10z

A: We have to find

Q: Vx² + 5 – 3 lim Find x² – 4 x2

A: To find the limit: limx→2x2+5-3x2-4 Solution: It is 00 form. So, we we will use L-hospital rule. In…

Q: Evaluate lim X→∞ √x-√x³-1 √9x3+3-4x

A: To evaluate the limit of the given function.

Q: n lim n (n+1) (n+ 2)² +. .+ is equal to - (2n – 1)

A: Given

Q: The value of lim (x³+2x4- 7x3- 5x²+ 11x – 15) X--2 (A) - 1 B) 1 2 (D -5

A: We need to evaluate limx→-2 x5+2x4-7x3-5x2+11x-15

Q: (b) lim In(5x2 +3) – In(2r² + 1). -

A: Given :

Q: 1– x2 lim r--00 3 + 2x – x3

A:

Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

A:

Q: (a) Evaluate lim, »∞ 3z+21 e 16

A: Given,          limx→∞3x2+2xex+6

Q: x-1 x-1+ √2x-x²-1 Evaluate lim

A: limx→1+x-12x-x2-1

Q: lim I+00 82-71 ||

A:

Q: 2 (x2+3) – 3 1- lim, 0 x2

A: To find limx → 0 x2 + 3 - 3x22

Q: 4x-x2 lim- x4X- 12 O 16 O 13 O 11 O

A: From the given problem:u   limx→44x-x2x-x   So,   limx→44x-x2x-x=4· 4-424-4=16-164-2=02=0

Q: How to evaluate this? lim 5x + 2 x→-1 lim 3x²-6x+1 x→4 lim √x²-5x+7 x→2 lim (-6x+1/8)³ x→1 lim…

A: As per our guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: 5x2 + 3 lim x → 1 x² + 6x – 4

A: Concept- limit x tend to 1 ,that means substitute the value of x=1 .