Find the particular antiderivative that satisfies the following conditions: dy 4а 2 + 6а — 2; у(1) — 6. %3| dx

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Q: 2. cos(arctan(1)) =

A: cosarc cosx =x

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (x³ + 1)² dx

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Q: 3. The diagram on the right shows an open box with a square base of side x cm and a height of h cm. ...

A: Use dervative

Q: Consider the scries > (-1)k (2k + 1)3* k=1 (a) Show that the scries is convergent. (b) Determine how...

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Q: 3. y?dx + (x² + 3xy + 4y²)dy = 0; when x = 2,y = 1

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Q: Question 1 Determine whether each series converges or diverges. Be sure to name the test 4n+1 (a) (i...

A: Since multiple questions are asked in multiple subparts. I am doing the first question only.

Q: Semio do 1. se h

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Q: d. When should the population be 999,999? Use the function from b. Write your answer ih a complete s...

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Q: S (5x - 3x + 5) dx %3D

A: recall: ∫xndx=xn+1n+1+C

Q: Σ -(2.r – 1)3". 14+1

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Q: Given the function f(a,9) = whose graph is shown belon. determine why the detnition of continuty at ...

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Q: Prove that the length of common chord of the two circles x + y² + 22x + c = (2² -c)(µ² +c) 2² + µ? O...

A: We will prove that the length of the common chord is the given term as following.

Q: olynomial graphed below -4 -2 -3 -4- y(x) =

A: Topic:- polynomial

Q: Find the Laplace transform for the follow e-t sin t

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Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-...

A: tanu = 5/13 other side of triangle = 194 cosu = 13/194 sinu = 5/194 sin2u = 2*cosu*sinu sin2u = 2*13...

Q: A truck is traveling due north at 55 km/hr approaching a crossroad. On a perpendicular road a police...

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Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y

A: area of the bounded by the y=1+lnx3x

Q: This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A i...

A: The given question has been solved in detail. 

Q: imum. Select the correct choice below and, if necessary e your choice.

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Q: To evaluate e"sin (e2^) cos(e2") dx. we let u=e* A True

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by par...

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Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x = 0, y= ...

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Q: Write an equation for the polynomial graphed below 4+ 2+ 2. -1 -3. -4- -5- y(x) = 2.

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Q: One car leaves a given point and travel north at 30 mph. Another car leaves 1 hour later, and travel...

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Q: Q4 A) What is the value of the limit of the function f(x) as x approach 0 x+2x-3 sinx + 4 <f(x) < x-...

A: Topic:- limits and function

Q: ta = ci + jand b = 8i + 15j. Find c so that the angle between a and b is ound your answers to four d...

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Q: Find the standard form of the equation of the ellipse and give the location of its Type the standard...

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Q: Consider the initial value problem y = sin(at), y(4) = 1 Use Euler's Method with five steps to appro...

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Q: 3. Evaluate each definite integral by using geometric formulas. (a) 14.x – 12| dr dr (b)

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Q: f(x) | f'(x) || g(x) | g'(x) -1 -7 16 -4 4 -2 1 -1 8 -1 10 11 Assume that f(x) and g(x) are differen...

A: Topic:- function and it's Derivatives

Q: dx y.= dy y arctan (-x 2a

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Q: -1.5z – 7 if I 2 4- -8 -7 -6 -5 -4 -3 -2 -1, 1 23 4 5 6 7 8 -2 -4- -5- -7 8- Clear All Draw: Note: B...

A: Topic:- function

Q: Write an equation for the function graphed below 4 -3-2 7.

A: We have to find the equation for the given graph. 

Q: The GDP of a certain country is $615 billion and is increasing by $25 thousand per person. The popul...

A: Given query is to find the rate of change of GDP.

Q: The sales functlon for a product is given by S(x) = 123 + 11.1x? - 0.1x, where x represents thousand...

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Q: In the following diagram, S represents the position of a power relay station located on a straight c...

A: In the following diagram, S represents the position of a power relay station located on a straight c...

Q: Question 1 [x sec(em) tan(en) dx= / x sec x² tan x² dx A True B) False

A: topic - indefinite integral

Q: Sketch the region enclosed by the given curves. x - 6y, x- 20 + y2 VAVA -3 -2 -1 2 -10 15 -25 -15 -1...

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region a...

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid generate...

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Q: A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are re...

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Q: Find the volume of the following solid. The solid above the region R= {(x,y): 0<x<2, 0sy<4-x} and be...

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Q: If f (x) = = |e*dx and f (0) =2, then what is f (2)? A) e+2 B В e2+1 e2 D e2-1 E) None

A: Explanation of the answer is as follows

Q: solve for the valve of IL that makkes the series converge nk

A: The given series is: ∑n=1∞7nnk Let, an=7nnk;n≥1

Q: Evaluate the definite integral. 1 xp 9 + (x + 5)2

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Q: Given that x- y2 = 9, then dy/dx =||

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Q: : Give the following formulas ① Volume and surface area of a sphere (diameter = a)

A: We know volume and surface area of a sphere

Q: II. Find There is no need to simplify. dr cos-(sin r) – sech(tan- r) 1. y = ecosh z 4r (log3 r) (csc...

A: Given problem:-   To find:-  dy/dx of given function