2 i (z-i) lim Z. z²+1 1 O 2i 1 - 1

Q: Find 23 + 8i (а) lim z-2i z2 + 4

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

Q: [()-](の) 4 3 |

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

Q: x³ – 7x + 6 lim x→1 x2 – 3x + 2

A:

Q: 42² (z−1)² 2 lim z →∞

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: Lim 5x−3 – 4 x→∞ 2x-2 + 9

A: Given,          limx→∞5x-3-42x-2+9

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: VI+x – 1 lim V4– x – V4– x²

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Q: lim (х — Vx? + х

A: Consider fx=x-x2+x. Simplify the above function. fx=x-x2+xx+x2+xx+x2+x=x2-x2-xx+x2+x=-xx+x2+x

Q: iz?-z- lim- z2-1 %3D i0 -i O 00

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Q: sin(8n) an 1 + Vn lim an %3D

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Q: 6n2 + 3n = 3 2n2 – 5 Prove: lim

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Q: Evaluate limx→−1 11/123 Does Not Exist O 0 O 1 2 x+2-1 x+1

A:

Q: 2 - x lim x-2 Vx + 2 - 2

A: we have to evaluate the following limit . For this we can use rationalisation

Q: 1 Find limxo (z-3) Select one: 00 O DNE

A: Using limit defition we get 1/infinity that is equals to zero

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: Fina the llmit or State that the lmit does not exist li Lim (I+ * 2. Lim (I+2X)

A: Explanation of the answer is as follows

Q: 1 3. lim 8 (t5 + 1)2

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Q: lim x²+3x sin x x-0 0 3 01 O does not exist 0 0

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Q: Sinx e* lim x→0 x- Sinx (b) If x = cos0,y = cosm0;m is an integer greater than unity, prove that %3!…

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Q: 6. Evaluate lim no 3n²-7n +41 2n² +42n- en

A:

Q: tan (x – 2) sin(r – 2)4 Evaluate: lim -

A: we want to find the value of limit   limx→2tan2(x-2)sin(x-2)4

Q: Evaluate lim X→∞ √x-√x³-1 √9x3+3-4x

A: To evaluate the limit of the given function.

Q: z1041 Find lim

A:

Q: z2 – 2z – 9zi – 8 – 18i - Evaluate lim z4+9i z2 – 4z – 9zi and write it in the standard a + ibform.…

A: The given problem is to evaluate the given complex limit, we have to check 0/0 form then we can use…

Q: sin (an) - 3cos² (5n) √5 n

A:

Q: т? + 2л — 8 lim с+2 х? — х — 2

A: Given: limx→2x2+2x-8x2-x-2

Q: 16-2 Evaluate: lim +4 V12+-a dne O 2 12 3 14

A:

Q: 1-z What is lim = ? !-2!- +2 1-i i-1 2 i+1 i-1 2i 2. 2.

A: Option (b) is correct

Q: In(x) − 4x² + 1 lim xxx² + 3x - 2√x

A: The given limit is limx→∞ln(x)-4x+1x2+3x-2x We have to find the value of the limit.

Q: x2 – 81 lim | I-9 x + 9 1 21 O -18 6- O 729 1 18 ||

A: Solve the limit.

Q: x² – 2x lim x+2+ [x] – x

A:

Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: 12 -9 V5r2 – 21 (а) lim I+3 1 + 2x – 15 (b) lim 10-т

A: We need to find following limits which can be calculated by simplifying the expressions and then…

Q: Vz - 3 lim z-3 z2- 9

A: We know,  limx→af(x)=f(a) a2-b2=(a-b)*(a+b)

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

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.