neither x² – 9 A) limx→3 4х — 12 - x2 – 1 - B) limx→1 VI – 1

Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: 2x +3 e that lim x2 + 5x 2

A:

Q: Prove rigorously that lim (4 + 8x) = -4. X-1

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Q: Describe the left end-behavior off (x) = x´+4x+ 1 o im *+4x+ 1 = -00 lim x²+4x+ 1 x²+4x+ 1 o lim = 0…

A:

Q: b. Find lim (xv (xVx²+1-x²)

A:

Q: Suppose lim f1x2 xSa o and lim glx2 = ". Prove that xSa %3D lim 1f1x2 + glx22 xSa

A:

Q: In(x-2) 1- Find , limx→2 In(x² -4)

A: Answer and explanation is given below...

Q: limits

A: Given,

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

A:

Q: Show that 2n lim n+2 = 2,

A:

Q: Evaluate: Vt2 + 3 – 2 lim - t→-1 t² – 1 - O Does not exist 1/4

A:

Q: what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8

A:

Q: Use the definition to show that 4n – 5 lim 2n + 3 - 2. n00 3.

A:

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

A:

Q: Prove using the formal definintion of a function that: limxto2 (5x + 5) = 15

A:

Q: b. limx-3= In(x-2) %3D X-3

A:

Q: 5. Find lim X00 ex2

A: given , limx→∞x3ex2 we have to find limit of given function

Q: Find the exists. 5 x а. lim 3 5x'+1 b. lim 10х-3x +7

A: Given that: a. limx→-∞5x-x3b. limx→∞5x3+110x3-3x2+7c. limx→∞5x2+2x2+3

Q: Prove rigorously that lim (4 + 8x) = −4. x→−1

A:

Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

A:

Q: lim (3x + 5) = 2, x→-1

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Q: бх — 2, х < 2 3. limf(x) for f (x) = x-2 %3D 13x2 -1, х 22 |

A:

Q: In(x-2) 1- Find , limx→2 In(x²-4)

A: The given limit is, limx→2ln(x-2)ln(x2-4)

Q: Use the e-8 definition to show that lim VI = 2. Z-14

A:

Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

A:

Q: ow that lim (x,y) → (0,0) 4 3x² + y² 5y does not exist.

A: To show that limit does not exist.

Q: Let –2x2 + 8x – 11 < f(x) < 2x² – 8x + 5. By using sandwich theorem, find lim f (x). x-2

A:

Q: limd x²-1 = X- T2+*]

A: Given questions:           Question 1:                                     limx→1+x2-1=?…

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find x→ -2 p(x). r(x) .…

A: Suppose that limx→-2p(x) = 4, limx→-2r(x) =0, and limx→-2s(x) =-3.

Q: 2. Rationalize lim(Vx² +1-x) -1- x

A: We have to find limit

Q: 2) lim X+1-x1 メーーt メーー 2x+2

A:

Q: b. Find lim (xvx²+1-x²)

A: Here, we take common x.then multiply denominator and numerator by √(x^2+1)+x

Q: In Exercises 28–35, find x+3 lim 21n- 2x+ 5 28. 29. lim 0 e -1 22 -2 +1 30. lim 2-1

A:

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: Show that lim +7.6' 3D7 3^+6^

A: Consider the given limit,…

Q: 1 is 68x+/68² x²+8x+71 lim→-0

A:

Q: If /6 – 5x2 sf(x)sV6-x² for - 1sxs1, find lim f(x). N6-5x² lim f(x) = X→0 (Type an exact answer,…

A: Solve by taking limit both side

Q: 8. find limx>2 x-2

A: We have to find the value of limit

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

A:

Q: Using direct substitution, what is lim²+6z_5, Z-2 223 O 1 O 1 O does not exist

A: We have to find    limx→2x2+6x-5x2-3

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .

Q: lim ( 7x 12 6. lim 13B

A: In this question we can find limit . Firstly solve quadratic equation of the numerator and cancel…