(a) Find 12x-2 – 7x8 dx. r4n+3 (b) Find the exact value of L. 2 cos(r – 1) dr. T+3

Q: (b) sinr + cos² y 4 P(품,등) 3

A:

Q: -T K/N 2 Cose de 1+ (sin)² -2pi 2pi Pi pi

A: Step 1: Given,∫−2π​2π​​1+(sinθ)22cosθ​dθ Step 2: Let's solve this by using u-substitution…

Q: Solve the ODE: (3e3 sin y-42y sin(7x)) dx + (e³ cos y + 12y cos(7x)) dy = 0 Entry format: Write your…

A:

Q: Find all solutions to cos(3nx) =

A: To find all the solution of: cos3πx=12

Q: (2) S dx x²√9-x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Which of the following equations are exact?

A: A differential equation of the form  called exact if and only if .

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

A:

Q: (c)(i) Use the substitution x = tan²0 to show that √x 。 (1 + x² ) ² (ii) Hence find in simplest…

A: We have to show                            ∫01x1+x22dx=∫0π42sin2θdθ     by substituting  x=tan2θ and…

Q: cos ( - i) = e2 + 1 2e e2 +1 e2 – 1 2e - e2 +1 2e

A: Givne that  cos(-i)

Q: Find the solution for L{e-3t(cos(5t) – sin(5t)}. Find the solution for L-1{E + 10}.

A:

Q: 8 csc? 4x cos(cot(4x)) dx sin² (cot(4x))

A: Here, I will be using method of substitution to solve this integral. You can assume:…

Q: Find all values of a for which the equation : 10х — 2л2 — а - cos (2x + a) = x² – 8x – C cos 3 has a…

A: Given equation is  cos10x-2x2-a3-cos2x+a=x2-8x-a               (i) First, let us solve the following…

Q: d 6. dx sine 1 sin(x²) (B) (D) – sint=") (A) – x sin(x²) (C) x sin(x²)

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Q: sec (x) e sin (x) dx ços x)

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

Q: 8 cos5(α)/(sin(α))1/2 dα

A:

Q: In(1+cos 3x) +C dx 3. 1+cos 3.x

A: Differentiate of the RHS the we get RHS

Q: tan(a+β) ; cosα = −(11/61) for α in Quadrant III and sinβ = −(63/65) for β in Quadrant IV

A: To find: tan(α+β)

Q: a 0.9062 Cos (1-√3x) dx = 1/2/2 : -0-1 a=0.5968

A:

Q: i. Find the domain and range of f(x)=2 cos'(4x– 3)–“ and sketch the graph 4 ii. Find the general…

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

Q: (-9)" (2n)! n=0

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Q: ly 3)[e^(-2y)]dy

A:

Q: Solve sin(6x)cos(11x) cos(6x)sin(11æ) = 0.2 for the smallest positive solution. Give your answer…

A: The objective of the question is determine the value of"x".

Q: Find for the following dx 1- cos² (x. y)= 2y³.x²-√√x+√√2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (a) v2x – 2 = Vx + 1; %3D -

A: As per our guidelines we are supposed to answer only one question at a time. So upload the other…

Q: Calculate the result of the operation B?f(x) ? If f(x) = 5sin(7x), B=-iº,where i = v-1. 1. A. -35i…

A: If fx=5 sin7x, B=-iddx, where i=-1Then to calculate the result of the operation B2fx.

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.