12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

Q: xe 1. lim, »o X→0 1-e*

A:

Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

A:

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

A:

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

A:

Q: Prove that lim, = 1, (x > 0).

A:

Q: (*+2x* -1) ? 5. What is f(-2) if lim, 5-3x 12 В. 6. C.- 15 D. -- А.

A: Given that: limx→-2x3+2x2-15-3x

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: Evaluate lim a,2)→(2,3) 2y2 +3xy 5xy+a?

A: This question is related to limit of function of two variables, we will use direct substitution…

Q: Calculate 14. lim (√x² + 1 - x). X18

A: Using series expansion about x =inf

Q: Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

A:

Q: Va – V22 lim x → 22 х — 22 - (Use

A:

Q: Determine the 3z 1 2x 1 2x 5 lim 00 O 00 2/4

A:

Q: b) Evaluate lim g(x) if 2x − 1 ≤ g(x) ≤ x² − 2x + 3 x→2

A: Above question is solved.

Q: Find the limit limx→∞(1+1x)3x.

A: we have to find the limit : limx→∞(1+x)(3x)

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: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

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: -(16*Z)x-(4*Z)- Evaluate the following: lim x→-Z x+Z

A:

Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

A:

Q: Inx 6. lim,

A:

Q: It alo, byo, show that lim (V(N+ a)(N+b)). -N

A: for a>0,b>0

Q: 3x lim х-2 V4х+1-1 4x+1

A: We can find the limit as below

Q: In x 6. lim, x

A: Solution:

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: lim In(10x) x-0t

A: To find the below right-hand limit.