P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2 = 0 is revolved about the line y = 2.!

Q: Find the following rates of change using a graphical method using the graph shown. a) The average…

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Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: dy 1+x²)²e³ = -2x dx

A: Topic:- differential equations

Q: (2x-1) dx 1 2x²³²-x²-27x +36

A: …

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Q: 9- a) Evaluate the following integral. b) Find the indefinite integral: S S₁² 5Cos(t) 3.Sin5 (t)…

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Q: f(x+h)-f(x) h Use f'(x) = lim h-0 s(x) = 6x+7 to find the derivative at x for the given function.

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Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

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Q: Find dy dx In y = e sinx Ody dx dy dx O dy dx O dy da - = = 1 = ye" sin x ye" cos x 1- ye" cos x yey…

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Q: How many square units is the area enclosed by y + 2x - 5 = 0, y = 4x - x² and x² - 4y = 0 ?

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Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

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Q: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² + 3x lim x-3 x² - 4x…

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Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: 17R(1,1,3), S(3,-3,6) and U(-2,4,7) are three vertices of parallelogram RSTU. a) Find the…

A: Given that the three vertices of a parallelogram RSTU are R1,1,3, S3,-3,6 and U-2,4,7 Now, let the…

Q: 2x² + y² +3z² = 1 y² = 4x x² -z² = y 2z = x² +4y² 2x + y − z =1 z = 4y²-x² E

A: We have to match the graph with equation and write name of these shapes.

Q: Let f(x) = 2.5x² - 2.2c. Use the difference quotient and h = 0.001 to estimate the slope of the…

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Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

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Q: If you apply the direct comparison test to assess convergence of arctan ²k, k¹.01 to which of these…

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Q: A rectangle is inscribed with its base on the x-axis and its x². What are the = upper corners on the…

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Q: tion f(x) given below, evaluate lim f(x) and lim f(x). X48 X118 f(x) = x + √√x² + 3 answer below:

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Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: 3-x x F(x) = (₂ + 1 (a) Find lim f(x) and lim f(x)? x-2+ x-2- (b) Does lim f(x) exist? why? x-2 x 3

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Q: What is the exponential growth rate change of an investment that has a b=1.92?

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: Given r(t)= , find the curvature. T

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Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: 4. Which of the following is an exact DE? A. (x²+1)dx-xydy-0 B. xdy+ (3x-2y)dx = 0 C. 2xydx…

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Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (8y² − x² + 7) dy = 0 s exact. If…

A: Topic:- differential equations

Q: Find the area of the region enclosed by the curves y=2 sin x y = 2 sin x and y=2 sin 2x for 0≤x≤ T.…

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Q: Question 13 What is the volume of the solid formed when the region bounded by the curve y=√16x², x =…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

Q: ſª √√√x – 1 dx is equal to 8 {A}-- 15 32 {B} - 15 - {c} {D} 8 15 32 15

A: To find out the integration.

Q: How to find a and b for a triangle when I only know that c is 15? (using the pythagorean theorem)

A: Concept: Pythagoras theorem: It states that the addition of the squares of the perpendicular and…

Q: x3 5x² Find the absolute maximum and absolute minimum of the function f(x) = + 4x + 2 over the…

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: 1. 2. 3. The degree of the differential equation (1²³²)² + (¹x² A. 3 C. 1 B. 2 D. not defined The…

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Q: The table shows the position of a cyclist. t (seconds) 0 1 2 3 4 5 s (meters) 0 1.3 4.6 10.4 17.5…

A: Average Velocity on a,b = s(b)-s(a)b-a.

Q: f(x)=0.2+25x-200x² +675x³-900x¹ +400x³ a=0 ve b=0.8 a.) find the integral by using Simpson 3/8 Rule…

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Q: (c) Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of…

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Q: 10- There is a rectangular playing field in Alaska Denali Park for a grizzly Bear with an area of…

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Q: 3) (11x + 17) dx 2x² + 7x - 4 S

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Q: 15. Solve for x: 37x+1=6561. A. 1 B. 2 C. 3 D. 4 16. If 3a = 7b, then 3a²/7b² = A. 1 B. 3/7 C. 7/3…

A: 15. The value of x such that 37x+1 = 6561 16. The value of 3a27b2 such that 3a = 7b

Q: 6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region…

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Q: Prove the limit below exists and find its value to 6 digits but replacing n for a large value and…

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Q: a. Find the lengths of the sides of a rectangle whose perimeter is 40 cm and whose area is 75cm².…

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