Prove: 1 a) lim Z+2i Z-1-21 b) lim 2-0 c) lim - 1 (Im²) ² IZE does not exist (Rez) 12-1 = 0

Q: [()-](の) 4 3 |

A: We simplify the expression to understand why is the result negative.

Q: Find the indicated limit. a) V3x+5-V5 lim a) b) x*+2x3-15х2 lim х-з х3+2x2-9х-18 b)

A: As per our policy we have to do only single question.  A) 3/(2√5)  B) 12/5

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

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

A:

Q: lim a. b. lim t-2 V2 + t – 2 t – 2 sin 7r с. lim 50 sin 3r 8 d. lim 16 16. V9r² + 4 lim 2.r + 1 е.

A:

Q: Let ginl=√1+an To find: (i) g'(x) cliij Domain of g(x) Domain of gix. Q using definition @ g'xl lim…

A:

Q: Find lim √√3x² + 3y² -1. (x,y) →(3,1) lim √√3x² + 3y² -1 = (x,y) →(3,1) (Type an exact answer.)

A:

Q: Prove that lim 1 H 101H 818

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

Q: 2) Calculate: a) lim- √x-3-1 x²-16

A: We rationalize the numerator and use the formula (a+b)(a–b) = a2–b2.

Q: Given that f(z) lim 2 2 - 1 = 3. Find (a) lim f(r) (b) lim f(x) +2- f(x) (c) lim - 2 (r2 – 1)7 (d)…

A:

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

A:

Q: lim x-0+ \x 1 = lim x2, 1 lim x0+ x2 1 = +0 - (+0) = 0 - - - -- %3D x-0+ x

A: It is infinity minus infinity type of indeterminate form.    To solve it first convert it into 0/0…

Q: Зп + 6ni ) lim n0 |2+ 3i|n

A:

Q: 2-x x+²√√x+2-√√3x-2 c) lim-

A:

Q: 2n2+3п-4 Find lim,→∞ . (show all necessary details) 3"

A: limit value = ?

Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

A:

Q: i) lim I-18 /976. T³ +1 Mar

A: Here is the solution:

Q: d) lim √2-x X-2+ 4 e) lim (¹2) x-3x-2

A:

Q: 5-V4+3s lims→7 7-s

A:

Q: x-2 j) lim -3x+2 3x+2x lim 0 x+4x k) x2 -3x+2 lim 2 x - 2x I) lim -x 1-x im m)

A: We will find the value of Given limit.

Q: 1.2) lim 1-/2г+1 x→0

A: Follow next step

Q: ( -4) a) 2-4x +3x b)

A: According to guidelines we should have been able to solve only one question at a time #a #b

Q: x < 1 then lim f(x) + lim f (x) =? f(x) = Inx , х21 x-1 x-

A: limit at a point exist if its right hand limit and left hand limit are equal and that value is same…

Q: c) lim (x – 7) x-7 f3x + 1, x< 5 lim x-5* (2x + 5, 5<x d)

A:

Q: Find the limits t +3 a) lim (4x3 – 3x² + x – 85); b) lim, t+2 t+1 ; c) lim x +0 1-V1+7x ; d) lim (7…

A: We can solve these problems in this way

Q: -3x + 4 a) lim x-2- x2 - 4 x2 b) lim x-3* x2 + 2x – 15 2x4 + 5x3 - 2х- 3 9x + 10 c) lim 5x7 + 2x6 –…

A: a) limx→2--3x+4x2-4=-3(2)+422-4=-6+44-4=-20=-∞limx→2--3x+4x2-4=-∞

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

A:

Q: Find: L . -im Z÷1+1 L Z²+1 2 Z²_1 im Z10 +1 7/0 14-Z 6 Z+1

A: (a). The given limit is: limz→1+iz2+1z2-1

Q: x² x-o ex-x-1 Evaluate lim А A) 0 B) 1 C) 2 D ∞ by applying L'Hôpital's rule.

A: find limit using L hospital rule option C correct answer

Q: 8.) lim (-1+ x² – x³ + 3x*) 9.) x3-2x-1 lim x-3 co-X 2x2+3x+1 lim X+ 3x-5x+2 10.)

A: