1. Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis. f(x) = 4x-x² 3 2 3 1 2 4

Q: Consider a hemispherical tank that is completely filled with water. The water exits the tank from…

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Q: 1. xex² dx ·6². 2.52²dx answer: answer:

A: ∫01xex2dxSubstitute u=x2→dudx=2x→dx=12xdu=12∫euduWe know that ∫audu=auln(a)=euPlug in the solved…

Q: An employee at a garden center fills a water tank once a day around noon to a height of 20 inches.…

A: Given: M(x)=5x3           T(x) =5x-103   where x in seconds

Q: Find f''(x). f(x) = (x²+6) 6

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Q: dy 2 +6y=3 dx y(x) = Give the largest interval I over which the general solution is defined. (Think…

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Q: Copy of Let A be the statement "Regine is Asian" and B be the statement "Mariah is American". Which…

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Q: 4) A coin is dropped from a height of 960 feet. The height, s (measured in feet), at time, t…

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Q: 17. A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the…

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Q: 0 3x - 4x 5× dx

A: We have to solve given Questions.

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: 16. A cup like object is made by rotating the area between y = 2x² and y = x+1 with x> 0 around the…

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: Using exact equation as given below:

Q: 2. For the quadratic function y = -6x² + (K + 4)x+ 9, find the following: a. The Axis of Symmetry of…

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Q: Find an equation for the hyperbola described. Graph the equation. Center at (8,-1); focus at (10,-…

A: Topic = Hyperbola

Q: Let G=7f-g, where the graphs of f and g are shown in the figure to the right. Find the following…

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Q: Find the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

A: Topic = Functions

Q: a) Find the simplified form of the difference quotient for the function f(x) = 2x² - 4x + 5. b)…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6 cos(t)i…

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Q: A doll sold for $253 in 1975 and was sold again in 1986 for $408. Assume that the growth in the…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Differentiate the function. G(x) = (x³-8). G'(x)= 2 x + 25 x²-25

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Q: дz (B)If Z = f(x, y), x= s² - t², y = 2st. Prove that s მs 2 (s² + t²) of əx

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Q: Find the derivative of the function. g(x) = (sech(7x))² g'(x) =

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Q: [1 if A= 2 13 2 1 -2 * find det (A) if 3 3 -11 6 O 38 O 16 O 18 O 48 O

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Find the indicated derivative. dy dt dy 11 for y=(2.5t-4t²) (2t+1.4)

A: Given that,   y=2.5t-4t22t+1.4

Q: 4) If y = 2√x - 2 tan-¹ √x, then y 1 -1 1+x²*

A: We have to find y' for the given function.

Q: Approximate the following integral using Simpson's rule. Experiment with values of n to ensure that…

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Q: Solve the given initial value problem. y" + 8y' + 25y=0; y(0)=3, y'(0)=-11

A: Our Aim is to solve the given initial value problem:-y"+8y'+25y=0, y(0)=3 , y'(0)=-11

Q: Calculate the integral SS²y-2x e²y-2x (y + 2x)³ dA R Where R is the region formed by joining the…

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Q: 24 S2−3x√1 + y² dydx 0

A: To solve the following iterated integral.∫02∫x24-3x1+y2 dy dx

Q: Sketch the graph of the floor function f(x) = [x+3] over the interval [-4, 2].

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Q: Find the inverse function of f(x) = √x −2+7. Specify the domain for f-¹(x) ƒ−¹(x) = (x − 7)² +2 -…

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Q: IF y = u² + 3u² & u = 2x Find d dx 8x(8x^2+3) (64x^3+30x) O 8x(8x^3+3) O 8x(8x^2-3) O

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Q: Find the limit. (If an answer does not exist, enter DNE.) x + 7-8 lim X→ 57 X - 57

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Q5) Solvex+2xy = 3 by using Euler's method to find he approximate solution up to X-2.9 when h = 0.5…

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Q: Find all vertical asymptote(s) for f(x) = r answers using limits. = √√7-√√3-x |x +41 (x2)) ●

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Q: 3. Determine whether the function is continuous at r = 5. 2²-42-5 2-5 x 5 D

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Q: how did you get y^2-4xy to y-4x when there are three y's on top I input the numbers and got 0 which…

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Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

A: Topic = Limits As per guidelines , At a time only one question can be answered. please repost for…

Q: The line y - 42-1457 is tangent to the graph of 111 at the point y=2x²-182²-158z+1

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Q: Estimate the area under the graph of f(x)=√x+2 over the interval [ - 2, 0] using eight approximating…

A: To estimate the area under the graph of fx=x+2 over the interval -2, 0 by using eight approximating…

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: A particle has position function r(t) and velocity function v(t) = { 2e“, sin(−t), ln(t+1) ) (a)…

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Q: The diagram below is an oblique, or slanted, rectangular prism. Not all angles shown are 90°.…

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Q: Evaluate the limit. lim (x,y) → (-5, -20) y² - 4xy y - 4x

A: Solve the following