iz³ – 8 lim z-2i z – 2i II

Q: (1) (2) I' = - R – I + 2 R' = I (b) Find lim→ R(t) and lim→ I(t).

A:

Q: Find the limits

A: Simply the value of limits have to be substituted in the eq. to find the value at the limits.

Q: (#1) lim (#2) lim (x,y)(0,0) x2 + y? (1,y)(0,0) (x2 + 2y6)2

A: ggg

Q: lim (2,1)→(0,0) xª + 4y²

A: The given limit is,

Q: 4 – x – y lim (1,9)→(2,2) I+y#4 T+ y – 2

A: Multiplying with conjugate:4-x-yx+y-2×x+y+2x+y+2=  (4-x-y)(x+y+2)(x+y)-4= -(x+y-4)(x+y+2)(x+y-4)=…

Q: z+ iz lim z+0 z+ iz equals .a None .b -i .C 1- .d i .e 1

A:

Q: iz³+1 lim z--i z²+1 3 2 ylgn ihi

A: Finding the limit by l'hospital rule

Q: lim (x,y)→(0,0) (x² + x²) (х, у) ->(0,0) а. 0 b. 1 с. 1/2 d. Does not exist

A:

Q: (2n +1) (п -1) (4n +1)(2n – 3) Evaluate lim

A: limn→∞ (2n+1) (n-1) (4n+1) (2n-3)-(i)Taking 'n' common from numerator and denominator, we…

Q: lim 2. I+,u ny 00

A:

Q: lim f(1) = 1, lim f(z) = – 00, I -2 f(- 2) = 1

A: Please see the below picture for detailed solution.

Q: Limits of compositions Evaluate each limit and justify youranswer.

A: The given expression is limx→0x8-3x6-140

Q: 1- 13 – z lim Z→2 Z- 2

A:

Q: |z-2 Find lin Z-2 |r-2| lim Z+2-2-2

A: Solution of question as follow

Q: lim (1,y) (0,0) (3 + (2² + y²) In(æ² + y?)) O 00 O 3 O does not exist 0 1

A: To find : limx, y → 0, 0 3 + x2 + y2 lnx2 + y2

Q: lim z approaches 4 ..............[z^2 - 10]^1/2

A: It is given that, f(x)=limz→4z2-1012   The solution of the given function is quite very easy because…

Q: Find lim [x +i(2x + y)] z→1-i iz3 – 1 lim z→i z+i

A: a) Given that, limz→1-ix+i2x+y It can be written as, limx+iy→1-ix+i2x+y

Q: lim z+0 z2 - 2sinz + 2x O 1 O 12 O 0 O 20

A: Let L is the limit value of given function .

Q: z+1 lim z-i z2+1 2 3A O

A: we have to find limit

Q: lim х2-36 V4x6+9х-1 а. х— -6 2х2+11х-6 lim b. х — 0о 11х3—2х2+1

A:

Q: 2 i (z-i) lim z→i z2+1 1 O 2i 1 -1

A:

Q: lim Ho eda + 2r lim 12/(1-1)

A: 1.. To find value of limit fist check weather it indeteeminant form or not. If it is in 0/0 or…

Q: lim (xn) 3a n ɛ N Xn+1 =;Xn + 2 ,x1 = 8 js iI + 2,x1 = 8 is isI %3D 8 O 4 2.

A: Let limn→∞xn = s then limn→∞xn+1 = s

Q: z² + iz lim z3 + 1 z- ob ||

A: We are given : limz→∞z2+izz3+1=limz→∞z2+izz3z3+1z3=limz→∞1z+i1z21+1z3=0+i(0)1+0=0…

Q: iz3 – 1 lim ス→i z+i

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (h – 2) - 4 (i) lim 2h

A:

Q: -2, I<-2 S(z) = 2- 2, -2 <z< 2 I22 f(-2) = f(2) =| %3D lim f(z) = lim f(z) = lim f(r) = -2 lim f(z)…

A: Use the corresponding piece-wise function to calculate the limits

Q: lim (i-8j+² k) 4 lim (r 1-8j+² k) = 1+ 16

A: We have to find the limit

Q: 8 d. lim 1+16 I-4 I- 16 V9r2 + 4 lim e. 2r +1

A: Explanation of the answer is as follows

Q: z3+1 lim z-i z2+1 3 A O 2.BO -2 .CO 3. N/3

A: limz→1   z3+1z2+1=?

Q: 2 i (z-i) lim Z. z²+1 1 O 2i 1 - 1

A:

Q: 2i (z-i) lim z?+1 1 - 1 1 O 2i

A: Consider limz→i2i(z-i)z2+1 = 2i(i-i)(i)2+1= 2i(i-i)-1+1= 00 Hence we will use L hospital's rule It…

Q: limtt 2 +z+1

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: z2+1 lim Z+i z*-1 3. 1 2. 1 20

A:

Q: 2 i (z-i) lim z →i z²+1 1 2i -1 | 1

A: Fourth option is correct.

Q: v3 – 8 lim 4 v→2 v* – 16

A:

Q: I-5 limr→2 1-2 1² –16 limr-4 1-3 lim,2 1²+3–10 I-2 I-2 lim

A: (a) limit as x tends to 2, the value of [(x - 5)/(x - 2)] is - infinity. (b) limit as x tends to -…

Q: lim sec In zis 2x Select one: a. T b. 2. C. d - 2/2

A: Given,

Q: lim (x,y)→(0,0) (3 + (x² + y²) In(x² + y´

A:

Q: 3 i(z³+1³) lim z→-i_z²+1

A:

Q: lim inf A, = {w : lim 1A, (@) = 1}. %3D %3D

A: We will use the definition to prove the fact.

Q: z²+ 1 lim ミ→i 24-1 i O -i O 1/2

A: To evaluate the given limit.

Q: lim z→0 2z5 (2)5 O None of these is equal to 2 is equal to 0 is equal to 1 O does not exist

A:

Q: lim (x,y)→(0,0) lim (x,y)→(0,0) 7x²+4y 4y 49x²-98xy+49y² 7x-7y

A:

Q: iz iz°+ 1 C - lim z -i z2 + 1

A:

Q: а. lim,(3r — 5) T-1 22 – 9 b. lim THe x2 – 4xr+3 where c= 0,1,2 22 – 9 C. lim 1→3 x2 – 4+3

A:

Q: I-1 lim I→1+ Vr²–1

A:

Q: iz3+13 lim z--i z2+1 2

A:

Q: 2 -z+1-i Prove that lim =1- :l+i z- 2z+2 2

A: solution is given below