(a) f(x) 15 for x < 2 for x ≥ 2

Q: 1) Consider the function g(x, y) = ln(xy). a. Find the domain. b. Sketch a graph of the domain. c.…

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Q: 3. Determine the equation of the tangent line to the curve: y = MacBook Air 1 2 3x² when x = -1.

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Q: ate the integral dx x² + 4x + 20 by completing the square and using trigonometric subs

A: ∫dxx2+4x+20 which can be written as  ∫dxx2+4x+4+16=∫dxx+22+42

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: 1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √1-x². (b)…

A: Solving the problem

Q: The population density (in people per square mile) of the city shown in the following figure can be…

A: The population density (in people per square mile) of the city shown in the following figure can be…

Q: Using algebra, find the point at which the line h(x) = (x, y) = = 2x + 0 intersects the line k(x) =…

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Q: (a) By using substitution method, evaluate (x²³ − 1)² dx.

A: The integral isTo determine: The solution of the integral.

Q: Express the set in interval notation. 3 Select one: O a. [3,9) O b. (3,9] O c. [3,9] O d. (-∞,3) 9

A: The number line represents the solution  the aim is to find the solution in interval notation

Q: Find the average value fave of the function f on the given interval. e¹/z z² 2 f(z) = [3, 5]

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Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

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Q: Problem 13 Find the solution of the initial value problem x' = Ar, with A- (₁₂2) and 2(0) = (-¹₁).

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Q: If $17700 is invested at an interest rate of 6 percent per year, find the value of the investment at…

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Q: Copy of Investigation - H... E Classes

A: Common Functions Function Derivative Constant c 0 Line x 1   ax a Square x2 2x Square Root…

Q: Write the pair of parametric equations in rectangular form. State any restrictions on t² the domain.…

A: To write the pair of parametric equations in rectangular form. To state any restrictions on the…

Q: c) f(x) = secx sin.x d) g(t)= cost t²

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

Q: S dx x√16x²-5

A: Let I is the value of given integration.Therefore I=∫1x16x2-5dx

Q: Consider the region bounded by the graphs of y = (a) Find the volume of the solid generated V = (b)…

A: According to question,Given Function,y = 2xx2+1

Q: c) (Vilntdt ; d) fe' sinxdx ;

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Q: Using row operations, find the inverse of this matrix. 1 -2 -61 [6] 01 5 001

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Q: 22. √₁² (x² – (2 (x² - 4x + 2) dx

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Q: Write a in the form r(t) = (2t+5)i + (-t)j + (-1²)k, t= -1 a=a+T+aNN at the given value of t without…

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Q: Nadia wants to get to the bus stop as quickly as possible. But The bus stop is across a grassy park,…

A: The bus stop is across a grassy park. It is 1500 feet west and 500 feet north of her starting…

Q: Write out the form of the partial fraction decomposition of the function (see example). Do not…

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Q: d the indefinite integral using integration by parts with the given choices of u and dv. (Use C for…

A: using  Integral by parts:-  ∫u v dx = u∫v dx −∫u' (∫v dx) dx  here u = ln(x) and v = x^3   u' = 1/x…

Q: Consider the following vector function. r(t) = (3t2, sin(t) - t cos(t), cos(t) + t sin(t)), t> 0

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Q: Given 2sin(x)= − 1, on the interval 10, 2], what is the value of x? 7개 11개 이뽕 {픔. ㅠ (픔·품] 6 6 7개 5개…

A: Solving the problem

Q: Problem #2: Find the derivative of 7x² - y¹⁰ = 25

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Q: -8 Find the formula for f. f(x) = 2,0 Hint: Transform an exponential function with an integer base.

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Q: Solve the initial-value problem for x as a function of t. dx (t2-10t+24) dt SAN 1, (t > 6, x(9) = 0)

A: Use the separated the variable

Q: Find the general solution of the given differential equation. dy dx y(x) = (1+x) - xy = x + x² Give…

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Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: Find the annual percentage yield for an investment at the following rates. (a) 7.1% compounded…

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Q: Solve the equation for n ny+ zp=nq+h

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Q: 7(6x + 1)³√√x² + x (6x + 1)5 x² + x 2

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Q: Find the vectors T, N, and B at the given point. T = N = B || r(t) = (5 cos(t), 5 sin(t), 5…

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Q: 2. Determine the derivative with respect to x of: a) f(x)=12* - 60

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Q: Let Σan (x+3)" n=0 denote the Taylor Series of 21 at the point x = −3. 2-x Then a5 =

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Q: 4 3 -3 +---)-(6) --- 00 0 12 0 A-1 = 120 A-21= 0 5 3 0 0 0 3 3 -3 -(6)-( 0 -1 0 1 2 -1 1 0 0 1 0 0 0…

A: ⇒A-I=43-3000120 ⇒A-2I=33-30-1012-1 ⇒A-4I=13-30-3012-3

Q: 10. Solve and check by integrating factor: {Integrating factor e[2(=)α = } y '+ 2 y = 4

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Q: The curves F₁(t) = (5t, t, 2t5) and 7₂(t) = (sin(-5t), sin(3t), t - π) intersect at the origin. 70 3…

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Q: Given the polar equation r The eccentricity is e = 9 8 + 5 cos(0)' The equation of the directrix is:…

A: Given the polar equation r=98+5 cosθ. To find the eccentricity, equation  of the directrix and to…

Q: In Problems 1-5, let R be the region bounded by y=x² + 3, y = 2x, x = 0, and x = 4. Each problem…

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Q: The base of a three-dimensional figure is bound by the line y = -x-2 on the interval [-6, -3].…

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Q: Use a table to find the Taylor polynomial P3 (x) for f(x) = √I-T around c = 2.

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Q: The position function of an object is given by s(t) = 16t², where s(t) is the height in feet and t…

A: We know that the speed formula ds/dt

Q: Decide whether the integral is improper. [In(x²) dx O proper O improper Explain your reasoning.…

A: The integral is  ∫1∞ ln(x9) dx

Q: Write out the form of the partial fraction decomposition of the function (see example). Do not…

A: The given function is, x4+5x5+3x3

Q: Given cos(8) = for << 플 thentan(0) = 3 +|m ○ -3 4 4

A: Given: cosθ=-35, π&lt;θ&lt;3π2 We are required to find: The value of tanθ.

Q: The owner of a skating rink rents the rink for parties at $440 if 20 or fewer skaters attend. For…

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