Which of the following describes the partial fraction decomposition of a rational function of the form 2x-3 f3dx? A Bd(x²) + C A B (2x) -+ x x² + 1 x x² + 1 O Option 1 O Option 4 A A - -+ + Bx C + x² + 1x² + 1 K -+ X Bx² x² + 1 + + C x² +1 C x² +1

Q: Suppose 0 <m(8)<, and x=2 sec(0). What is the resulting expression if we write √x² - 4 as a…

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Q: 0 00 00 Consider the function f: (-2, 2)→ R defined by Mex X 6t D = S(x) = [₁ = [₁₁125²4d² - dt -…

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Q: Differentiate. 7 - 6x +2e¯x + +X y=xe Choose the correct answer below. O A. dy dx OB. dy dx OC. dy…

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A: Given that ,              density of the liquid ρ = 8232 N/m3                          side of…

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Q: Evaluate the following integral 1. y4+2y²-1 √y dy; y to 2. f(−4t + 12) (5t +15)dt

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A: answer is in next step

Q: Use substitution to find the indefinite integral. 16t-8t² dt (1-1) e 16t- ... Describe the most…

A: Solve the following

Q: 0# 7' 7P VE 1-₂72 +67

A: topic - indefinite integral

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Q: Using Rationalizing Substitution S O Arctan(y) + C Ⓒ2Arctan(y) + C O In(y) + C O2ln(y) + C dx X√√x-1…

A: The integral is  ∫ dxxx-1=∫f(y)dy

Q: What are the amplitude and period of function? y = 1/cos x

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Q: A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6…

A: Explained below

Q: Lim g-bot (e³+g) 1/9

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Q: lim (et + t)¹/t t→0+

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: We have to find volume about y=-1

Q: 1. The shaded region in Figure 1 is bounded by the curve x = y² + 2y and line x = 3. Which one of…

A: topic - area bounded by curves

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Q: In each item, set up an iterated double integral that gives the volume of the solid described. (a) a…

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Q: Evaluate the iterated integrals. 2 yz b. So So So xyz dx dy dz Jo 0 0

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

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Q: 7. Differentiate y = log10 (x² + 1)² b. 4xlog10e x²+1 a. 4x(x² + 1) c. log e(x) (x² + 1) d. 2x(x² +…

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Q: A plane flying horizontally at an altitude of 2 miles and a speed of 510 mi/h passes directly over a…

A: Given problem:- A plane flying horizontally at an altitude of 2 miles and a speed of 510 mi/h passes…

Q: 3. 4. x= F7 ←x=1 20

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Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

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Q: Find the point of intersection of the terminal side of the angle 11 with the unit circl 6 Ⓒ (-1/2/3…

A: Solution:

Q: Differentiate. g(x) = log 23 (5x-4) g'(x) =

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, the total…

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Q: 1. Encuentre la ecuación del plano determinado por los puntos P(1,2,3) Q(2,3,1) R(0,-2,-1) 2.…

A: Vector equation of the plane passing through the three points with position vectors a, b and c is…

Q: Iff and g are continuous on [a,b)], then [*[f(x)\g(x)]dx = [[*f(x)dx)(√*g(x)dx) a A True B) False

A: If f and g are continuous on a,b, then ∫abfxgxdx=∫abf(x)dx∫abg(x)dx

Q: Set-up the integral for the area of the plane region bounded by y=x+4 and y=x²-2x (x²-3x-4)dx (5+…

A: The given region are:y=x+4 and y=x2-2xTo find the area.

Q: 1) Determine what comes next in the given pattern and provide solution/explanation: 72 11 20

A: Topic:- sequence and series

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: Using Rationalizing Substitution 5y+5+ 5 y-1 6 6y+6+ y-1 6y²+6y+6+ 1 y²(y-1) 6 y-1 .729 dx 64 √x-3√x…

A: We can solve the given integral.

Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A: we know the work needed to stretch the spring W=12kx2 where x is the elongation. x=xf-xi=45-30=15…

Q: A street light is at the top of a 10 ft tall pole. A woman 6.5 ft tall walks toward the pole with a…

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A: Here, the area bounded by the curve f(x)=8-2x2 ; [0,4] is as shown below:

Q: 3- Determine f"(x).. F(x)= cosx cotx

A: This question is related to differentiation, We will solve it using given information.

Q: The demand for a certain type of cosmetic is given by p= 160-x, where p is the price in dollars when…

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Q: Using Rationalizing Substitution a=4, b = 9 a = 8,b=27 a=64, b= 729 a=2, b=3 729 S 64 dx √x - √√x =…

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Q: Using Rationalizing Substitution S- O In(y) + C O Arctan(y) + C O2Arctan(y) + C O2ln(y) + C dx…

A: ∫dxxx-1Substitute y=x-1→dydx=12x-1→dx=2x-1dy=2∫1y2+1dy

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A: We have to find the limit

Q: √x+1 Using Rationalizing Substitution ·S= -dx = y2 + 4y+ 4in(y-1) + C, express the final answer in…

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Q: Note: Volume of a cylinder is r²h, where is the radius and h is the height. A closed wood storage…

A: Volume of cylinder= πr^2h

Q: 1+x² 1. Find the area of the region bounded by the curve y=- 2x² and the lines y = 0, y = x, x = 2.

A: Given problem:-  1. Find the area of the region bounded by the curve y=(1+x2)/2x2 and the lines y =…