What is the average value of f(x) between x = 0 and x = 2 for f(x) = 1.609 0.805 0.693 O 0 2 2x+1 ?

Q: dy dx -5y=-tr, 5y = ³ 2 y(1)=1

A: The given differential equation is  dy/dx -5y= -5/2 xy3 , y(1)=1

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Please answer completely. Step by step. Evaluate. 2 [² (4-x²)³/2x² dx

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Q: Suppose the Maclaurin series of a function is f(x)=2+3x+2x² + x³ + x² + .. Find the first four…

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Q: Example 6: Show that a a² 1 b b2 b c c2 Solution: L.H.S a a2 = = - (b - c) (c - a) (a - b) c 1 b b2…

A: Topic = Determinant

Q: What is the total change of f(x), if f'(x) = 4x² + 6, over the interval [-1, 2]? -18 ထို့ကြ ကြ O O…

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy 2 +y √( 1 ) = 3x²y² =…

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Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

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Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: |2x+4| lim x->-2+ √x+2

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Q: Use the Ratio Test to determine whether the series convergent or divergent. Σ n=1 Identify an…

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Q: Please answer completely. Step by step. Evaluate. S arccos x dx

A: I have stated the used formulas in the solution

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

A: Let f be a function for t≥0 then the integral Lf(t)=∫0∞e-stf(t) dtWe have to find the Lf(t)Where…

Q: Compute each of the following limits. alim √5x²-16 X4-4 2x²+x-1 a. lim x4-1 4x+4 4x²-6x-5 lim…

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Q: 1) Find all intercepts and test for symmetry. y = 3√9-x

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Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x — axis, the limits…

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Q: Tutorial Exercise Find the derivative by the limit process. f(x) = 14 - x² Step 1 Complete the…

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Q: The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 6, 12…

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Q: e. Find the second derivaitve. f''(x) = f. Use parts b through e to identify maximums as points. g.…

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Q: Example 3.6.2 Sketch the graph of y = f(x) = (2) Answer: A. The function is not defined at 3, so the…

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Q: Find the derivative of the following functions. F(x) = √²** 1. √/20162). 2. G(x) = 3. H(x) = L √t³ +…

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Q: Evaluate the integral using the following values. 8 ["x³ dx = 960, ["x dx = 24, ["dx-4 = J4 8 [²- x…

A: Gievn , Hint: 4∫8xdx=24   .....(1)

Q: dy Prob. 5 (a) ( ....) Given the curve x³ - xy² + y³ = 1, use implicit differentiation to find da at…

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Q: Consider the function f(x) = x² - 98x² + 4, −6 ≤ x ≤ 15. This function has an absolute minimum value…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 20-x²;…

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Q: Which of the following formulas would be used to calculate the trapezoid approximation of 0.2 3 0 T₁…

A: Here we using trapezoidal rule.

Q: Find F(s). F(s) = L{(1 et + 5e-3t)cos(6t)}

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Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: we have to find limit of function  here function is given y = x x =4 and x axis  x axis means x = 0…

Q: Use the Laplace transform to solve the given initial-value problem. y" + 5y' + 4y = 0, y(0) = 1,…

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Q: a) Let f(x)=-3x² + 4x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 1 + est L{f(t)}

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Q: Solve y(1): dy/dt + x = 1; dx/dt -y + 4et = 0; x(0)=0 and y(0)=0. 6.33 4.89 O 7.10 3.51 O 1.80

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Q: In the following exercises, use direct substitution to show that each limit leads to the…

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

Q: ƒ f(x) = 25, find f'(-3).

A: Topic:- derivatives

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: The graph shown below is f (x) = √√9 - x². If g(x) = f* f(t) dt, what is g′ (√5)? g' 00 02 O 2.5 5+…

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Q: S² (4-x²)³2x² dx

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

Q: Question 6 of 11 (Use symbolic notation and fractions where needed.) minimum: Incorrect maximum:…

A: Given: the graph is given then we have to find the value of the value of the A

Q: Consider the following given function and given interval. f(x) = 10 sin(x) - 5 sin(2x), [0, π] (a)…

A: Given data÷ fx=10sinx-5sin2x Interval : 0,π   From part a) the value of favg=20π   fc is given by…

Q: Find the total change of f(x) between x = 1 and x = 4, when 1.25 0.75 0.25 -0.75 df 1 dx x2 =

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Q: 17. On [1,2], f(x) has an absolute minimum value of 257 (A) (B) -58 (C) 18. f(x) has a relative…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: 7 The volume of an ellipsoid y + + fixed, show that the ellipsoid of maximum c² 4πabc 3 volume is a…

A: Ellipsoid : x2a2+y2b2+z2c2=1Volume of ellipse : 4πabc3a+b+c is fixed

Q: Evaluate the integral using the following values. [x³ dx = 320, ["x dx = 15, ["dx-4 = dx

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