[In (a* + 3) – In (2r* –- 1)] In (2r³ – 1) 7. lim

Q: Which of [0], [1], [2], [3], [4] is equal to [3]^2023 in Z_5? What is [15]^1989 congruent to in…

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Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 –…

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Q: 8. lim x - 4 + In (x – 4)

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Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a>0, n∈N and B=1+na

Q: If g(t) = £? (e-35-*), a farmula for L (e* g14) is? -8t +8 a) ede+25 b) e 3e+17

A: Given g(t)=ℒ-1e-3s-7

Q: Give a combinatorial proof of the identity (2)=3(") + ³(²) 3(3).

A: The combination formula is defined as (nr)=n!r!(n−r)! Therefore…

Q: 4. In(4i)

A: complex number

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

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Q: 6n2 + 3n = 3 2n2 – 5 Prove: lim

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Q: (ii) w* +1 – 8(@) TOEY 4 2.

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Q: Use the binomial theorem to expand the following: (a) (x + 2y)* (c) (3x + 1)4 (b) (x - y)6 (d) (x +…

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Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

A:

Q: x(x²+1 V2x³ –1

A: to calculate thefollowing expressionlnxx2+122x3-1

Q: Could you please explain what happened in b and where the 1/2 came from

A: The formula is given by:       xn+1=xn2                         ..........1 Using equation (1), we…

Q: 10 [1] Find the coefficient of the term involving x* in the expansion of (3x - a. -262444 b. -262440…

A: We have to find the coefficient of x^4.

Q: form of (3+3i)^5

A: Given,      (3+3i)5

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: 5-V4+3s lims→7 7-s

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Q: 1.) (2a* –be)(ša² +3bc) (x*y-5z')(x*y–42*) 2.)

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Q: (4x*) for all x#0? Show the manipulations that lead to your 5. Which of the following is equivalent…

A: Explanation of the answer is as follows

Q: 201-25-(1-82 60 86)(So) | (o-Sh)는 (0-5h4

A: Do square both the side. Now solve 5 powered equation.

Q: 3 O Find the first three terms of the expansion of (1+x)(2x-1)

A: The given series is 3(x+1)(2x-1) We have to find first three terms of the given series. This can be…

Q: x2 dx is (ax2+4)(x2+9)

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Q: dx (1)(- 2e * )

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Q: [ *(1 + 2') dt = 1 + 2°) dt 14 + C In(7) In(14) 14t+1 In(14) 7t+1 + C In(7) 7t In(7) 9t + C In(9) +…

A: Given:       ∫ 7t(1+2t)dt

Q: Find [7]^-1 in Z55 under multiplication.

A:

Q: Evaluate: (3 e + 9* – 7) dr =.

A: Given : ∫3e3x+9x-7dx

Q: 2-¹ {881 (0 -₁)} = athert sen(8t), (8-8)²+64, What's the value of a*c?

A:

Q: For what value of k is x+1 a factor of x^4+2x^3-3x^2+kx+1 in ℤ_5[x]?   1 2 3 4 None of the above

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Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

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Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.