Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

Q: L sin2t cos3t

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Q: Question 1 C(0, -3,-1). Consider the points A(2, -1,0), B(3, 0, -2), and (a) Find the equation of…

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. [3, for x = 1, for x * 1 f(x):…

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Q: Evaluate [/3 cos(x) In (sin(x)) dx T1/6

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Q: (9) The differential equation M(x, y)dx + (2ye* + y²e³x) dy = = is exact if (a) M(x, y) = e2x y² +…

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Q: Find the general solution of the given differential equation. 3 +24y = 8 dy dx y(x) = Give the…

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Q: :.S •√ √x(x² – 3x + 2)dx

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Q: Calculate the derivative. y = tan -T y = 2+x 2 - x (Express numbers in exact form. Use symbolic…

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Q: Find the derivative of the function y = 4 sec¹ (x + 2). (Use symbolic notation and fractions where…

A: We can find the derivative as below.

Q: The line L with symmetric equations point P(3,-3, -2). Select one: True False x+3 = = passes through…

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Q: The Eigen values of the matrix A = = 1 1 li 1 0 1 1 0 0 1 0,1,2 O 0,0,1 O 0,2,-1 O 0,-1,2 O 0,2,2 O

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Q: Question 1 C(0, -3,-1). Consider the points A(2, -1,0), B(3, 0, -2), and (a) Find the equation of…

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find 2; -2 lim x→0- f(x) and O…

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Q: Matrix has only one row call Row Matrix. multiply a matrix (A) by another matrix (B) if the number…

A: We check the given statements are True or False.

Q: Maximize B=2xy2, where x and y are positive numbers such that x+y2=10. The maximum value of B is…

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Q: Question 2: A) Verify that y = c₁e-x + c₂e5x is a solution of the DE: y" - 4y - 5y = 0. B) Find a…

A: Topic = Differential equation

Q: Use the graph to determine whether each statement is tru lim f(x) exists. x → -3 -5 -4 -3 -2 -1 -1…

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Q: Evaluate the definite integral. 2 cot-¹(x) 1+x² 1 - 1 -dx

A: To evaluate the integral.

Q: A rectangular lot has an area of 1600 sq m. find the least amount of fence that could be used to…

A: Solution of given question is written in below steps.

Q: Let a = (5, 4, 2) and b = (-1, -2, -3), then 3a 5b (10, 2, -9). = - Select one: O True O False

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Q: By using trapezoidal rule, n=2, The integral = π/2 sin (x) dx 0.9444 O 0.9481 O 0.94809 O 0.9482 O…

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Q: Solve through finite differences with four subintervals: + y = 0, y'(0) + X(0) = 2, dr² x ( + 7) + (…

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Q: H.W: replace the following polar equations by equivalent Cartesian equation, then describe or…

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Q: S In (x) √xln(x)-x -X dx

A: ∫ln(x)xln(x)-xdx

Q: 3. Solve below definite integrals (a) [²3test d (b) ["* dt, 3tedt, ["¹ (c) In(x) -d.x,

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Q: Solve the system of equations by any method. -2x + 5y = −35 7x + 2y = 25 Enter the exact answer as…

A: We use the elimination method to solve the given system of equations.

Q: The Maclaurin series of the function f(x) = 8x² sin(8x) can be written as f(x) = Σ" 72=0 where a few…

A: Solution is given below:

Q: 5. r² = 1

A: As per the rules of the company we can answer only first question and rest can be reposted.

Q: 4T (2n)-T(n) 4. Use Simpson's rule to approximate I'v = 3 2x3³ +23dx with S(40). Use the formula…

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. 11 K √x + 5dx = [Please enter your…

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Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

A: Using Laplace transform

Q: 5. Evaluate the improper integral S₁ 1 (x-3) 5/3 dx.

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Q: x cos 3x dx

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Q: If a xi = 0 and a x j = 0, then Select one: O a is equal to i + j a cannot be determined O a is…

A: Find out the correct option.

Q: Find the total area of the shaded region shown to the right given by the curve y = 2( sin x)√1+…

A: We can solve this as follows:

Q: 1 A = 1 1 * The Eigen values of the matrix 0 1 1 10 1. 1 10 0,2,-1 O 0,0,1 O 0,2,2 O 0,1,2 O 0-12

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Q: Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the two…

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Q: Part 1 of 3 (a) Graph f(x)=3|x for x S

A: Solution ) f(x) = 3 |x|  x<0 Vertical dilation of scale factor 3 f(x) = -3x and x<0

Q: Using Homogenous Equations solve in terms of y: (x² + y²) y' xy

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Q: 38. The amount of P 20,000 was deposited in a bank earning an interest of 6.5% per annum. Determine…

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Q: A fast-food restaurant has a cost of production C (x) When does the company start to turn a profit?…

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Q: (a)[1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

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Q: Find a linear differential operator that annihilates the given function. 2.3 + e* cos 2x

A: Let, the given function:fx=3+excos 2x

Q: Situation 1 (items 43-44). For the beam and loading shown in Figure 2, determine the following: 44.…

A: We have to find the tension in cable BC.

Q: Choose the angle (in radian) between the following two vectors u = and U = - O 2.059 00 O None of…

A: We know that the angle between two vectors u and v is θ = cos-1 u·vuv

Q: 2. Find the area of the region inside the cardioids r = a(1+cos), a>0

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Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

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Q: Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 8. For the telescoping series find a formula for the nth term of the sequence of (2k-1)(2k + 1)'…

A: The telescoping series ∑k=1∞22k-12k+1

Q: S: x²(In x) dx

A: We can find the integration as below.