Q6/(A)Evalute √2² £2ª ex² dxdy.

Q: Solve the given differential equation. All solutions should be found. dy 2xy + y² +8 x² + 2xy dx…

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

A: The solution is given below

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

A: Graph the given floor function

Q: Find the solution of the given initial value problem. π ty' + 2y sint, y = 1, t > 0 Y || =

A: In this question, we want to find the solution of the given first order non-homogeneous linear…

Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…

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Q: Find the solution of the given initial value problem. ㅠ ty' + 2y = sint, y (-) - = 5, t > 0 Y ||

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Q: 2 2 J 1 2 3

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Q: Find the inverse function f¯1 of the function f. Find the range of f and the domain and range of f T…

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Q: Consider the function f given below. 2 X-9 f(x)= = x-3 a) For what x-values(s) is this function not…

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

Q: 55,000 Suppose that the demand function for a product is given by D(p) = and that the price p is a…

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Q: 1. g(x) = Sin 39 COS 32 5 ㅈ

A: The objective is to differentiate the equation.

Q: Differentiate. G(x) = (2x² + 7) (9x+√x) G'(x) =

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Q: State the order of the given ordinary differential equation. d²y dx² dy = 1+ dx. Determine whether…

A: We know that :-  The ORDER of a differential equation is the order of the highest  derivatives that…

Q: 0 3x - 4x 5× dx

A: We have to solve given Questions.

Q: Q4: A conical tank with Diameter of (2 m) from the top and (5 m) height. At the bottom of the tank…

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Q: y=0 x=y ye dxdy=

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Q: S₁ y² – 3ydy 11

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Q: R: y² = 4x, y = 4, y -axis

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 7x)y², y(0) = 2…

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Q: lim x-0 1 1 (ex ²-₁-²) 1

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Q: Question 3. The following figure shows the graph of the derivative f' of a function f, where f is…

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Q: 1 (c) I Y (d) y = 5x x², y = x = 0, y = 1, y = e I=

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Q: Find the inverse function of f(x) = = Specify the domain for f−¹(x) ƒ-¹(x) = x² - 9 Domain of f¹(x)…

A: Given that,

Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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Q: Calculate the work (in joules) required to pump all liquid out of a full tank. Assume a = 6 m, b =…

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Q: Multiply the following fractions using the array model method described in the video lesson. Make…

A: First we will understand the process and then solve it.

Q: Given the graph of fx), determine the range of f(x) • 8 -10-9-8-7-6-5 OR O(-1) (1.) O(-2) u (2) O(1)…

A: Range of an inverse function is the domain of the orginal function.

Q: 6y²dx − x(2x³ + y)dy = 0.

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Q: Find the general solution of the given differential equation. x²y' + xy = 8 y(x) = Give the largest…

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Q: 8. Use the Integral Test to determine whether k4 Σk5 +55 k=1 converges.

A: Solve the following

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x = 1,…

A: Topic = Volume

Q: B) Evaluate the line integral of the function P(x,y) dx + Q(x,y) dy. over the curve C where…

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

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Q: A particle start from the point (4,4) and it's coordinates change by the increment AY=5 and AX= -8…

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Q: Find the arc length of the curve y = 2/3 (x − 1) raise to 3/2 on the interval [2,3]

A: We have to find the arc length of the given interval [2,3] .

Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

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

A: Use total derivative and chain rule

Q: Find an explicit solution of the given initial-value problem. √2 √1-y² dx - √1-x² dy = 0, y(0) = 2 y…

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Q: Find the derivative. 2 f(x) = 8√2x +9 f'(x) = [

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Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

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Q: Show that the following equation [ has a solution on (0, 2). 42-1 = πX 2 5 cos(-

A: The given equation,       4x-1=5cosπx2

Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)-0 Find y(0.1)?

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Q: Find the solution of the given initial value problem. ty' + - 2y = sint, y(7) = 5, t > 0 y =

A: For the linear differential equation of the form: the general solution is given by: where

Q: Evaluate the integral. 1 u5 1 [(4-3- du u √√2 5 1 --- 4 3 1 √2 du = (Simplify your answer.)

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Q: Find the logarithm. 1 log 4 256

A: The given logarithmic expression. log41256 As we know from the logarithmic rule: logaab=b The…

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: State the order of the given ordinary differential equation. ty(6)t5y" + 5y = 0

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

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