To find the volume formed by the function z=f(x, y) = x²y over the triangular region bounded by the lines x = 0, y = 0 and x+y=2, set up the double integral.

Q: Let v(t) = (t², -4t,9). Compute the derivative of the following function. v(e¹)

A: Solve the following

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: Q6) Test the convergence of the following 3) Σ=1 (n!)" (nn)²

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Q: Use the graph of f to evaluate the following: 6 + f(x) 5 X 4 رها 3 N 1 1 2 4 5 The average rate of…

A: Equation of slope:  Slope =(y2-y1)/(x2-x1) The average change of the function over the given time…

Q: Express as a sum or difference of logarithms without exponents. 5 4 X log c 4_7 y'z What is the…

A: log(a^n) =n(log(x))  log(a/b) =loga- logb log(ab) =loga +logb

Q: y = (x²+4)* Use Logarithmic Differentiation to find dy dx = dy dx

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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 volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

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Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: Follow the steps below for the given function. xy5y - 8 = 0 Solve the equation for y. y = 8 x-5…

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Q: 1. Let A = 24 12 -40 20 and consider the linear system = AY. Let Y(t) be the solution 5 What is the…

A: answer is in next step.  i can answer only one  question as per guideline thank you.

Q: Find the indefinite integral on the domain of positive real numbers. Enter an exact answer. Remember…

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Q: find the area.  x^2=8y and x=y+1

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Q: 3 -21 3 -1 The Cofactor Matrix is :- -3 0 [-3 0 12] 606 6] 36 ن من من IF A [-3 0 12] 606 3-6 6…

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

Q: -0.5 1 100³S 1-=X² dx represents the area of a region bounded by 1 O a. the vertical lines x = +0.5,…

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Q: 13. The graph of y = f(x) and y = g(x) are shown below. g(x) 6 (a) (b) f(x) 2 10 -2 Find h'(9) if…

A: Explained below

Q: Calculus I Find the second derivative.

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Q: Consider the position function below. r(t) = (1-16,5-4t²) for t≥ 0 a. Find the velocity and the…

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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: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x sin x n = 1 f'(x) n = 2…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ = dx 7x +…

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Q: Show that |7₁7₂|=|z₁||2₂|

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Q: Solve by Gaussian elimination x-4y-2z = 21 24y + 2 = 3 3x+2y-z = -2

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Q: If f(x) is linear, g(x) is linear, and h(x) = f(x)/g(x) What is the maximum number of vertical…

A: fx is linear, gx is linear and hx=fxgx

Q: 8. Find the area bounded by y=ex, y=x² and x=2. a. 3.1 u² b. 4.1 u² c. 5.1 u² d. 6.1 u²

A: Here we have to find the area bounded by the given curves.

Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

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Q: Find the domain of the following vector-valued function. r(t) = sin 5ti + ²√² + ¹ k e

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Q: To say that x + 5| ≤ 3 is the same as saying is in the closed interval [A, B] where A is: and where…

A: The objective is to find A and B.

Q: 04:B/ Simplify Moivre's theorem? [cos 30+ i sin30 15[cos 0-i sine 1³ [cos 50+ i sin50][cos 20-i…

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Q: 6 6 Suppose ff(x) dx = −4 and g(x) d -4 3 3 6 Evaluate (3 f(x) — 3 g(x)) dx. 3 Remember to include a…

A: Given that ∫36f(x)dx=-4   and ∫36g(x)dx=-3 we have to calculate , ∫363fx-3gxdx. To solve this…

Q: 2 6. For the telescoping series find a formula for the nth term of the sequence of (2k + 3)(2k + 5)'…

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Q: 4. Find the limit of the sequence 3e" + 20n 6e +37 7} or determine that it diverges.

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Q: ſº 5u³ – 3u³ – 9du

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

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Q: Differentiate the function. (2x+5) y= (5x+1) 3 기 dx 11

A: Given:       y=2x+545x+13 differentiating with respect to x Apply the quotient rule:…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

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Q: Find the integrating factor u(x) and solve the differential equation (integrating as a total…

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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: Solve the given initial-value problem. Give the largest interval I over which the solution is…

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Q: 2.) (cotx + tanx) ² dx

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Q: 1 Sz Find the indefinite integral S[=1714 14 X 17 0 dx = 3 X 14 X 14 X 1 3 dx.

A: Solution : Given that indefinite integral is

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

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

Q: Q4) find the soluation of differention equation using exact equation 2) 2xy' = 10 x³y5+ y

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Q: 1. Let f(x) = sin² (x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin²(x) cos³ (x) π Based on the graph,…

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Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 4x + 3 y = 16 where x is the…

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Q: Find a basis for the null space of A = [³3 -3 1 2 -1 -2 4.

A: The given matrix: A=3121-3-1-2-1.We need to find a basis for the null space of A.

Q: WEEK 8 LESSON 3: Finding Circumferenc 0 LEARNING TASK 1 Ma'am Rona, Reese's teacher saw Piolo and…

A: Given Diameter=4m  Radius=2m  Solve the learning task