3x + 1 Evaluate (x-1) (x+2) dx using Partial fractions.

Q: If you apply the direct comparison test to assess convergence of 1 - to which of these series would…

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Q: If [ f(x) dx = 12. g(x) dx = -2 and L₁ dr following gives the value of [[1²)+ 4 76 Sh +4g(x)- h(x)…

A: Given:     ∫-36fxdx=12     ∫-36gxdx=-2     ∫-36hxdx=-7

Q: P1: Calculate the area bounded by the curves: C. y e* and x - 2y + 5 = 0, and y-axis.

A: To calculate the area bounded by the following curves.y=e-x and x-2y+5=0, and y‐axis.

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: Differentiate the following expression: y = x² cos 4x

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Q: Given: y = = 4 cot (3 - 2x) Find: dy dx 0-8 csc² (32x) O csc² (3-2x) 08 csc² (3-2x) -4 csc² (3-2x)

A: Given y=4cot(3-2x)To find dydx:

Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

Q: *An Integration factor of the following differential equation dy (x log x) + y = 2log z dx Option 3…

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Q: Find the number in the interval [0,3] such that the difference of its square from its cube is the…

A: Given problem:- Find the number in the interval [0, 2/3] such that the difference of its square from…

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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Q: Find the midpoint of the line segment shown below. 6+ 4 Midpoint 11 224 -4 5 -6+

A: We need to find mid point.

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

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Q: 4x* dx

A: We need to solve the following. So,            ∫-224x4dx=4·∫-22x4dx=4x55-22=4·645=2565

Q: Consider the following initial-value problem. f'(x) = 8ex − 4x; f(0) : = 13 Integrate the function…

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Q: Exercises A write the 1st 4 terms 1. >. र 2641 0:4 [(-₁)^(²) 2. 2. I

A: Given that infinite series is

Q: if X(z) is the z-transform then what is the z-transform of x(n) of x(n- ?6)

A: In this question, we need to find the z transform of x(n-6).

Q: TT sinx sin 2x dx 2 cos x

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Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be confirmed…

A: Follow the procedure given below.

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: A giant spherical-shaped snowball is melting. If the radius decreases at the rate of 0.5 in/min, now…

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Q: Its tot as TR = 300q - 6q² and its total costs as TC = 4q². a) Determine the optimal quantity and…

A: Given

Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: What is the z-transform of the ?signal x(n)=(0.5)nu(n) Roc |Z| 0.5 Option 1 1 (1-0.5z-¹) 1…

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Q: Obtain the sum of the seri Ean $a = -² 2 n=2 nn

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Q: 3 A box with a square base and open top must have a volum of 108000 cm³. We wish to find the…

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Q: CD is a parallelogram with vertices A(0, 2, -3), B(2, -1, 4) and C(-3, 1, 2). Find the angl een the…

A: Follow the procedure given below.

Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: To find out the levels of x and y which will maximizes the utility.

Q: 3.) The natural length of a spring is 8 inches. A force of 20 lb stretches the spring to 10 in. Find…

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Q: ƒ(x) = x0.03 1 f(x) = X0.35

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Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: Given the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q²-20³…

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Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below:

Q: Prove that the following functions u/v are harmonic; then find the conjugate harmonic function v/ u.…

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Q: The volume generated by revolving the first-quadrant area bounded by the parabola y2 = 8x and the…

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Q: 4. The equation of a plane is [x, y, z)=[-1,-1,1]+s[1, 0, 1]+[0, 1, 2]. Find the - intercept of the…

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Q: 3 s²+1 6 s² + 1 Option 4 O * The Laplace transform of the x(t) is x (t) = 3 sint 3 s²+2 6 s²+2…

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Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: This question is related to Functions and application of integration, we will solve it using given…

Q: (*). (1) without a calculator. We will do the followings: 1.2.3.4 7.6.5.4 = 2.3.4 7.6.5 7.5 = 1 I…

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Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

A: Here we have to choose the correct option.

Q: Use the Laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t,    y(0) =…

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Q: c) y(x) = c₂x² + ₂x Q20) The form of a particular solution of y"-4y' - 12y = sin(2t), is: . a) y,…

A: Using inverse operator

Q: Find the point(s) on the surface y2-xz = 4 that are closest to the origin and find the minimum…

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