3u4-7u Find the most general antiderivative of f(u) = Note: Any arbitrary constants used must be an upper-case "C" F(u)

Q: Question 2 a. I b. | function f(x, y) = y² − x² + — a 1 Find the critical points of the function…

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Q: xy' = y + x²

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Q: 2. Consider M(x, y) + N(x,y) · = 0. (a) Suppose we can find a function F example of such an equation…

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Q: X-0.5 Let X - Bernoulli (0.5) and Z = 0.5. If Mz (t) is the mgf of Z then Mz (1) = %3D 0.5

A: Solution: Let X~Bernoulli(p= 0.5) The mean of X is  μ= p=0.5 The standard deviation of X is…

Q: 1.0 1,0 -1 =) 5f(x) dr = %3D =) L 5f(x) dr =| =) S* 5f(x) dr =| ) | 5f(x)| dx =|

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Q: 4. (i) The function f is given by f(x) = x+1 (x-1)(x2+1) Express f(x) in partial fractions. Hence…

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Q: lim (1, y)→(0, 0) (r + y +9)e-1/(z²+v²)

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Q: 3. (a) The trapezium rule for integrating a function over the interval [-h, h] can be written in the…

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Q: 2х + 1 The antiderivative of f (x): is (x – 3)? (x – 2) x - 2 A F (x) = 5 ln +C x – 3 x - 3 B None…

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Q: 1. Find the function M(x, y) and its degree 2. Find the function N(x, y) and its degree 3. Is the…

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Q: 1-e y = f(x) = ln fonksiyon eğrisinin x = 2 ve x = 4 apsisli noktaları 1+e-x arasındaki yayının…

A: The arc of the curve is given as:

Q: 1) Let X and Y have the joint pmf defined by f(x, y) = where x = 1,2 and y = 2,4 a. Solve for c. b.…

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Q: -but + 1/u Find the most general antiderivative of f(u) = u? Note: Any arbitrary constants used must…

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Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 1 (2) Suppose that g(x) is an antiderivative of and g(1) = 3. 2 Va3 What is the value of g(4) ?

A: Given:        Let fx=-12x3     g(x) is the anti-derivative of f(x).       By anti-derivating  the…

Q: 2.x +1 The antiderivative of f(x) = is (x – 3)² (x – 2) 2 7 +C 3 A F (x) = 5 ln 3 | 3 + 2 В F (x) =…

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Q: (a) Find the antiderivative F(x) of the function f(x) = x° – e* + e, that satisfies the initial…

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Q: 3. Evaluate: Use gamma or beta laws 00 | e-x2+2x dx (Hint: let t = (x – 1)²) 0.

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Q: Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k…

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Q: (1,0), and (1,5). 5) Find the potential function of F(x, y, z) = (e² + ye*, e* + ze³,e³ + xe² ).

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Q: 1. Applying continuous differentiatíion, which of the following functions have a set of linearly…

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Q: 1 1 Select all the antiderivatives of f(x)=-+ %3D x² +1

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Q: 7. Find the most general antiderivative of the function 9 (z) = - z² +1

A: We use Trigonometry substitution to find anti derivative

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: 2 2х-4 2у — 1 dydx x + 1 ) Q2. Evaluate the double integral

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Q: In the spring equation F = k x, the spring force, F is called Group of answer choices an independent…

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Q: Question 5 What can you derive by applying Associativity (Assoc) to F~O • X)

A: In the given question, the concept of associative property is applied. Associative Property The…

Q: 20-21 >> MTH 113-1 (Lec) >> Calculus 2 Consider the function f(x,y)=2xy-x2+y2+7y3. It has 2 critical…

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Q: 3. Find the integrating factor e∫Pdx then find the general solution. 2(y - 4x2)dx + xdy = 0

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Q: DETER Derer mine the fieSt os: mine the キ)12ST oこ: derivative F6) = aresee(3x) %3D

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Q: 4. A company provides earthquake insurance. The premium X is modeled by the p.d.f. f(x) = 52e °, 0<x…

A: A company provides earthquake insurance. The premium X is modeled by the pdf f(x) = x52e-x/5  ,…

Q: Find the antiderivative of f(x) = x++7

A: Given,         The antiderivative of fx=x3+1x2+7

Q: III. Elimination of Arbitrary constant. 3. xcos(xy)+ e* In y = c

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Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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Q: 2 3 4 5 ven the graph of f(x)above, determie the average rate of change of f(x) from x = 1 to x = 5.

A: we have to find

Q: (1 - Vx)? 1 –. Do 1 -1 -1/2 - X Use rules of antidifferentiation to find an antiderivative F(x) of…

A: Integration

Q: Activity 1. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: 21 4, [ V IA IV M How can I help you? show that u (x,t) = sin(x + sin t)is a solution to the partial…

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Q: A fish population in a lake satisfies dB/dt=cB(K-B) Fish are then added at A fish per hour.  Find…

A: Please check step 2 for solution

Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: (f) xy' = y² +y ху

A: # we are entitled to solve one question at at time, please resubmit the other question if you wish…

Q: 6. Solve the first-order linear DE + 3x2y = 6x2 by using an integrating factor. (a) Hint:Remember…

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Q: 5.2-9. Determine the constant c such that f(x) cx (1 – x)°, 0 < x < 1, is a pdf. |-

A: Given: fx=cx3×1-x6        0&lt;x&lt;1