The region R enclosed by the curves y=x and y=x^2 is rotated about the x-axis. Find the volume of the resulting solid. Soln in handwritten

Q: 22-12x x²(3x² - 10x-8) To solve - for this integral? a dx partial fraction is to be employed. What…

A: Partial fraction

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Q: A clothing business finds there is a linear relationship between the number of shirts, n, it can…

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Q: 1 2x²-3 √² ²3 dx = (x² + 3)² + ²x² ³ + d x+√√x²+3 27 x²

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A: We are aske dto find the curvature and radius of the curve.

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Q: 13. How many times will you perform integration by parts to evaluate sin(Inx) dx? A. 1 B. 2 C. 3 D.…

A: Let's find.

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Q: ƒ dx = f(+ g(x)) dx, then A + f g(x) dx is equal to x³+x A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

A: Given that,

Q: Find f(x) if f'(x) = f(x) = 20x - 99 Of(x) = 20x² +1 O f(x) = 20x + 25 +5 Of(x) = 20x f(x) = 20x + C…

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A: We know that the upper base of the basketball looks like a circle therefore we will use the formula…

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Q: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: x = 48 cos(t),

A: answer is in next step

Q: f(x) = 6(x-6)2/3 +8. (A) Find all critical values and list them below. Note: If there are no…

A: topic - functions and derivatives

Q: Use the information given below to find sin (a-³). 12 tan a = with a in quadrant III I 5 3 cos B =…

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Q: dx secx+1

A: Given ∫dxsecx+1We do half angle substitution:=∫1tan2(x2)+11-tan2(x2)+1dxSubstitute…

Q: ||r'(t) x r"(t)|| 3 ||r' (t)||³ r(t) = t²i+t¹³j Use the formula k(t): = k(t) = = to find k(t).

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Q: b) f4 sec 0 tan 0 do

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Q: 23. Choose the correct answer. A lemon is launched into the air, and its path is recorded by a…

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Q: Compute the area bounded by the curve y=3x² and the lines y=0 and x = 3,

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

Q: Find the radius of convergence, R, of the series. 8 n Σ (x-a)", b>0 bn n = 1 R= Find the interval,…

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Q: Find the exact value of the trigonometric function of using the given format: 5T Let 8 = then is in…

A: I am attaching image so that you understand each and every step.

Q: d d Calculate[ri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and…

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Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

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Q: 3 (1 – 6x) C4 = Find the radius of convergence R = Represent the function f(x) = ➤ Cnxn n=0 Co = C₁…

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Q: Using integration by parts, Then k is? (a) - 1.5136 [x² cos(x²) dx = k - [*x sin(x³) dx fx 0 (b) -…

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Q: Find a power serie CAPS |||| Determine the interval of convergence. (Enter your answer using…

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Q: Find the exact value of the trigonometric function of using the given format: 5T Let 8 = then is in…

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Q: b) fex-c - cos x + 1dx

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Consider the integral f sin-¹x dx. If we let u = sin ¹x and dv = dx, the integral can be written as…

A: The given integral,  ∫sin-1x dx

Q: dx 1+tan x

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Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy-1)² 2…

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Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

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Q: Find the area of region bounded by the graphs of the equations. 1. y = 5x² + 2, x = 0, x = 2, y = 0

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Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: In 2 Use the formula t= that gives the time for a population, with a growth rate k, to double, to…

A: We need to find growth rate and time to double the population.

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Q: What can you say about the series Σan in each of the following cases using the Ratio Test? Answer…

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Q: Find the inverse of f(x) f-¹(z) = . ✓ 3z + 1 -3x+4

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Q: 3) f(x, y, z)=x² + y² -2=²+ = ln(x). (1,1,1) -1/2 4) ƒ(x, y, z)=(x² + y² + =²)¯¹¹² +ln(xyz),…

A: 3)    fx,y,z=x2+y2-2z2+zlnx We have,       grad∅=∇f=i∂f∂x+j∂f∂y+k∂f∂z ∂f∂x=2x+zx ∂f∂y=2y…

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A: The given equation is: t2+t+19=0

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A: We have to find the equation of the tangent.

Q: Given the price-supply function p = S(x) = 10(e0.02x - 1), find the average price (in dollars) over…

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