What is f (x) of f(x) = 320 (2x-7)³ O4x²-28x-31 (2x-7)¹ [(8x-28)-4(4x²-28x-31)] (2x-7)¹ O4x²-28x-31 (2x-7)² 2x² +52-27 2x-7

Q: Solve the initial value problem: dy dz 9y, y(0) = 1

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Q: Evaluate the indefinite integral 9ds s ln(88)

A: We can solve this as follows:

Q: converge

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Q: A spring requires 7 J to stretch from 1m to 4 m. An additional 4 J to stretch for 4 m to 7 m. What…

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Q: Find the general solution of the differential equation. y(4) + 2y″ + y = 7 + cos(2t). NOTE: Use C₁,…

A: To find the general solution of the given differential equation.

Q: dy 3. Find X by implicit differentiation. √x+y+√xy = 4

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Q: Find the area of the shaded region. (-11/4, 11/2) 10 y 8 x = y² - 6 y 6 4 -2 x = 5 y-y² 5

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Q: Write the first five terms of the geometric sequence. a 1 =  -5; r = -3

A: We can find the first five terms as below.

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.…

A: We have to find area of given region.

Q: 1. Describe what it means for a relation to be a function. Provide an example of a function, and…

A: Description given below with example

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: The partial derivative with respect to x of the function f(x, y) = x²y + cos y + y sin x ? Select…

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Q: he method of variation of parameters to determin on of the given differential equation. y"" — y'′ =…

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Q: 1 SSR (x+y)² dxdy

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y(4) +…

A: We have to find the suitable form of Y(t).

Q: Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the…

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Q: Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=36-x². Graph the…

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Q: e² 1+2e +e S Select one: O A. dx 1+6² 2 1+6² +C +C O B. OC. +C OD. +C -2 Ite -1 1+e

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Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: We need to find the sum of the first five terms of the geometric sequence:  4/3, 8/3, 16/3 . . .

Q: Integrate the given function (Handwritten) tan2x + 2x^2x

A: Here we use basic formula of integration .

Q: Find the sum of the first 11 terms of the geometric sequence: 7, -21, 63, -189, 567, . . . .

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-1)^-1_57 47n3 n = 1…

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Q: Population of a certain country is growing exponentially at a rate of 1.5% per year. How long will…

A: Given problem:- Population of a certain country is growing exponentially at a rate of 1.5% per year.…

Q: Write 2x (x+1)² constants. completely in the form of partial fractions solving all the unknown + v…

A: Given problem:- Find partial fraction of 2x/(x+1)2

Q: Find the critical value 5x+1/x

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Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx

Q: Get the interval and radius of conv this given power series (x - 3)" n

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Q: 1. Determine the area of the region under the curve y=x√(x² - 1) 2. Determine the area of the region…

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Q: For the following exercise, use logarithmic differentiation to find dy dx y=xcotx

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Q: Work problem 30 Given the vector function 5 F(1) = (61³ – ¾, sec(4 − 1)), t then find the tangent…

A: Given :Ft=<6t3-5t, sec4-t>at t=4

Q: To evaluate the integral 1. 7 64 + x² -dx,

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Q: 5. Use the definition of Taylor series to find the first four nonzero terms of the Taylor series for…

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Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Here we have to find the limits and then state whether it diverges or not.

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

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Q: y (4x + y) dx -2(x²-y)dy = 0

A: Let's solve given diffrential equation.

Q: Calculus I Find d^2y/dx^2 for x + y^2 = 3

A: Solving the problem by finding the value of the problem.

Q: Set up the definite integral required to find the area of the region between the graph of y = = x² y…

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Q: The velocity of an object is shown in the graph below 5 4- Velocity (m/s) N 1 3 Time (sec) Submit…

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Q: If f is a differentiable function and % up on Selected Answers: (0,1) f'(x)=x5 − 5x4+ 5x³+2, then…

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Q: The number of oil changes per hour at Quick Lube is described by the following short-term production…

A: answer is in next step .

Q: Which of the rectangles below are right rectangles? 25-4 20 15 10 63 BODEX 0 5 10 15 20 25 Select…

A: This question can be solved using the concept of estimating the area under curve using left and…

Q: = Which of the following represents the shaded area between y J(a) and y = g(x)! 8 6 2

A: We are asked to find which is represented for shaded area between the curves

Q: The graph of the function w = f(x, y) is shown below. (a) Assume that x and y are functions of a…

A: Given :w=fx,y

Q: (hex) = (7x-6x³) 9 2) 3) x+1 x-1 x√x+1

A: Find the derivative

Q: Use Newton's method to approximate a root of the equation 2 sin(x) = x as follows. 1 be the initial…

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Q: Question 1 Let C be a curve defined by the vector equation r(t)= <8t³ - 9t, 8t³ +7t, e8³-917. Show…

A: Solve the following

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: The current population of a small town is 2848 people. It is believed that town's population is…

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

A: We have to find the work W required to pump the water out of the spout.