4. Let ao 3 and an+1 = 2an + 12 an + 1 Find lim an n→∞ = a.

Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

Q: 4. a. Evaluate lim x - x-6 x→3 x2 -9 x+1 lim x→-1 /3 - x –2 b. Evaluate

A:

Q: Show that lim Z-2 (2-2)4 || ∞

A:

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

A:

Q: A) Vx2 +8-3 lim x-1 x+1

A: By using l'Hospital's rule we solve the given problem as follows :

Q: lim. Vx-1 х2-4) п-20+ \x2-4

A: To find the Value of

Q: Show that - lim→∞ Xn = limn→∞(-Xn).

A: The objective of this question is to prove that the limit of a sequence multiplied by a negative…

Q: 7x If h(x) = (1 + 4)¹x, find lim h(x) X→∞

A: In the question is :h(x)=1+4x7xlimx→∞hx=limx→∞1+4x7x

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A: We have to prove that  limx→0- 1x → -∞.

Q: lim X+ X+)X +3 2x-X-1

A: Given: The function is  f(x)=x3+x2+x+32x3-x-1   To determine: limx→1x3+x2+x+32x3-x-1

Q: 8+x-4x? Lim\ belowr → 0∞ V6+x²+7x* O a. -4/7 O b. 4/7 O c. 4//7 O d. -4/7

A:

Q: Find lim (1+ I-X 4 T

A:

Q: Зх— 6 Find Lim x-2 x? - 4

A: We have to find:  limx→2 3x-6x2-4

Q: Find the one-sided limit

A: Given: limx→-12+6x2+x-14x2-4x-3

Q: (込) 6. (d) lim x→3x-3 x² -9

A: Find the limit . Of [1/(x-3) -6/(x2-9)] when x tends to 3

Q: 4. Find lim (x² – 9)/(x² – 8x + 15)

A: To find the limit of given function.

Q: Find the value of a so that √x²-5x = 4 Vx2 lim √x² + ax - X18

A: We are required to find the value of a for which limx→∞x2+ax-x2-5x=4

Q: Inx 6. lim,

A:

Q: Gal Evalunte the fallowing: O lim 1 +31-10 1-5

A:

Q: 7. Use the ɛ, 8 -definition of a limit to prove the following limit. lim (az +b) = azo +b, for…

A:

Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: 2a? Find lim a→-I a² - a –2 а -2

A: topic - limits

Q: 4. Use the &, 8 definition to prove that lim (4x-1) = -9.

A:

Q: 3. Let f(x) = 3 - X, 82 X +1, x > 2. 3 x < 2 0 y = 3-x 2 y=2+1 4 → X a. Find lim,2+ f(x) and limx-2-…

A:

Q: 2. Find lim n→∞ N (e-(a/n) - (2a/n) + e -(3a/n) + e + . e-(na/n)).

A: To find the following limit.

Q: In(2+x) lim, x+-1 X+1

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: b) 49-(5+ x)² x-2 lim-

A: Use L.Hospital rule to evaluate above limit as in next step.