CHECKPOINT 3.14 √ √ Rewrite the integral evaluate the integral). x³ √25x² dx using the appropriate trigonometric substitution (do not

Q: 23: Solve the initial value problem 2√ = cos² (y) and y(0) = 2. lease write your answer in the form…

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Q: Consider the following autonomous first-order differential equation. =y² - 2y dx Find the critical…

A: Given differential equation:- dy/dx =y2 -2y

Q: Question 2 Choose the correct answer. The average rate of change of the function f(x) = x² + 1 from…

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Q: Evaluate using Reduction Formula 1. f cos7x dx 2. f sin³x dx cos x x dx n cos-1x sinx + 1 sin" x dx…

A: We use the given formula for sine to evaluate the given integral. But the given formula for sine is…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Let's solve given differential equation.

Q: Σ +∞ + 1 + sin2 η 10η in=1

A: Given Series,∑n = 1∞1 + sin2 n10n

Q: For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously.…

A: Given f(x, y) = 5x3 − 14xy + y3 Fomulae: ddx(xn)=nxn-1 and ddx(x)=1 By differentiating it with…

Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t², y = 9+ 4t³,…

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Q: (a) Find the derivative of f (x) = (x² + 2) (4x − 3) by first expanding the polynomials. Enter the…

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Q: Find the solution of the given initial value problem 88y" +19y" + y = 0, y(0) = -5, y'(0) = 6, y"(0)…

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Q: The table below shows the velocity of an object (cm/sec) at each sec as it moves along a track for…

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Q: Use the figure to find the exact value of the following trigonometric function. tan (20) tan (20) =…

A: We can find tan(2 theta) by multiple trigonometric formula.

Q: Ted is driving east at 80 km/hr and Anthony is driving north at 50 km/hr. Both cars are approaching…

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Q: Determine the length of the parametric curve given by ㅠ = cost, 0≤t t≤ 2. X = sin³ t, y

A: To determine the length of the parametric curve given by x=sin3 t, y=cos3 t, 0≤t≤π2.

Q: Evaluate the integral: r+∞ 1 dv v²+2v-3

A: We will find the integral.

Q: For the function 1 - 3x x² + 2 find the values of the following limits: f(x) = lim f(x)= [Select]…

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Q: If f(x)=√x+7 and h(x) = 6 -, find f(x) + h(x). X

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Q: Solve the initial-value problem for x as a function of t . (2t³ − 2t² + t − 1) 12, x(2) = 0 dx dt =

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Q: Sketch the region enclosed by the given curves, y = 3x² and y = x² + 4. Find the area of the region.

A: Given curves are y=3x2 and y=x2+4.

Q: Evaluate the integral: -2 y√2y-y²dy

A: A detailed solution is given below

Q: 3. Find the equation of the plane containing both the point (1, 2, 3) and the line r(t) = (t, 2t+1,…

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Q: Fill in each blank with an angle between 0° and 360° such that sin 200° = sin and cos 200° = COS

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Q: Calculating Second-Order Partial Derivatives Find all the second-order partial derivatives of the…

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Q: ∞ Σ (tan ¹5k-tan-1 (5k-5)) k=1 ∞ The series Σ (tan k=1 -1 -1 5k - tan (5k- -5)) can be tested for…

A: Given :∑k=1∞tan-15k-tan-15k-5

Q: An open-top storage box with a square base has a capacity of 32 m². Find the dimensions that will…

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Q: The rate for parking in the short-term lot (maximum of 12 hours) at the seaport is $1.50 for the…

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Q: Write an equation for the polynomial graphed below 4 3 2- M -5 -4 -3 -2 -4 -5 + y(x) = 7 7 2 + 4 +…

A: To find the equation of polynomial from the graph

Q: problem for x as a function of t. Solve the initial-value dx (t² − 10t + 21) = 1, (t > 7, x(9) = 0)…

A: The given equation is;  (t2-10t+21)dx/dt =1 (t>7, x(9)=0)

Q: (x + y \(xdy+ ydx)– xy(xdx+ydy)=( +y²

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Q: ermine whether the sets S₁ and S₂ span the same subspace of R³. S₁ = {(4, 3, 4), (0, 4, 4), (8, 10,…

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Q: Solve the right triangle with hypotenuse 28 and one of the acute ngles 42°.

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Q: Solve 8 sin (7x) = 7 for the four smallest positive solutions

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Q: If 0 = sec (0) csc (0) = 1 -π, enter exact value for each function. 6 = tan (0) cot (0) = __ 0002

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Q: Solve: f b. Od In(Ink) dk 2k (Ink) In[In (Ink) - 1] Ink [In (Ink)-1] In(Ink)-1 k In (Ink) - 1

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Q: If f(x)=√10- x and g(x) 3x² 10 - 3 x²√10 x - O 3√10-x x² X Ox²√10-2 3 O None of these. 3 g(x) find…

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Q: (b) 3x + 11 S 2 -dr x²-x-6

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Q: 10. Prove: cos²(x)-sin²(x) =sin² (x) 1-tan²(x)

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Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

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Q: A truck with 22-in.-diameter wheels is traveling at 45 mi/h. Find the angular speed of the wheels in…

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Q: The Cartesian coordinates of a point are given. (a) (-2, 2)

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: The function f(x) = ,30 ≤x≤ 100, models the tax revenue, f(x), in tens of billions of dollars, in…

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....)…

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Q: Use numerical or graphical evidence to determine the left and right hand limits of the fund |32 -…

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Q: It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars…

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Q: 1. 8. (v³ - 3y + 2)√√9+x²dx + x²dy = 0 (x² - 1)y" + 2y' — (x − 1)(x + 1)² = 0

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Q: Q1 (a) Show that y= Ae²* + Be ³*, where A and B are constants, is the general solution of the…

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Q: 1) tan x Find the derivative of y= = e

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Q: [ see³(z) tan³(x)dx

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Q: 1. The point (-2, 5) lies on the circle whose center is at (-1,-3). Write the standard form of the…

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