Q.4: Determine the intervals of the function F(x) = 2 x - 7x + 5 for whichf(x) 2 0. %3D

Q: Solve the following Dife rential equations. 1. (xy+y")y' = y

A: Topic:- differential equations

Q: sin x cos“x tan® x dy Given that y = find using dx logarithmic differentiation. dy dx ||

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Q: 6. Find k such that the line is tangent to the graph of the function f(x) = k/x and y = 2x + 18.

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Q: The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown...

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Q: Find domain a 1 f(x,y)= (1/xy) 2 f(x,y)= sqrt(y-x^2)

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Q: Find the distance between the complex numbers in the complex plane. 5i, 6-4i

A: Distance formula in the complex number : d = (c-a)2+d-b2 where a+ib and c+id be given complex number...

Q: Write the first five terms of the sequence with the given nth term. = sin 2 %3D 4. 5.

A: To write the first five terms of the sequence with the given nth term.an=sinnπ2  

Q: Select the correct equation for the following graph: 10- 5- -10 5- 10 5- -10- 2x-6 O f(x) 22 +x-2 f ...

A: find the equation for given graph

Q: N- My If- = R, where R is a function depending only on the quantity z = xy, then the differential eq...

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Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following equatio...

A: x2+2y2=kf(x, y, k) = x2+2y2-k =0differentiating w.r.t  x,2x + 4y dydx-0=0dydx= -x2ysubstitute -dxdy ...

Q: Let x, Y be positive real numbers. If x2 – y² =1, then x or y (or both) is not an integer.

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Q: The domain of the function 7 (t) = (In t, cos 2t, /t – 2) is

A: Given that function rt→=lnt,cos2t,t-2To find : Domain Solution: rt→=lnt,cos2t,t-2t>0,t-2≥0

Q: Consider the function f(x, y) with level curves as shown below. At the point P are two vectors ū and...

A: Explained below 

Q: Using double integration, find the volume of the solid bounded below by the plane z = 0 and above by...

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Q: solution

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Q: Findy ot x-5xy+3y =7 Oy= 2x-5y 5x+6y 2x-5y 5x-6y 2x+5y Oy 3x+6V 2x+5y Oy- 5x-6y

A: Given y² - 5xy + 3y² = 7 To find y':

Q: y' = 2aye (5)² 2 y²+y²e(#)¨+2»²e÷) 2 +2x?e(7)

A:

Q: 16 Fill in the blanks. Non-vertical lines have ___________________ slope. Decreasing lines have ____...

A: for vertical line there are no slope  and for non vertical line we cant say about slope because it i...

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate...

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Q: suppose that f(x) is a function with f(150) = 49 and f '(150) = 3. estimate f(154). f(154) = ____

A: To solve the given problem use the following formula. f(x) = f(x0) + f '(x0) (x - x0)

Q: Match the following improper integral with the improper integral below in which you can compare usin...

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Q: give

A: We have to choose the correct options according to the given information

Q: 4 3. 4 -3 2 -1 3 6. 8. -3 Given the piecewise function above evaluate the following statements. (wri...

A: topic - limits

Q: . Evaluate the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

Q: When you are using the Midpoint Rule with n =3 to approximate x*dx. a) ]: What is Ax? Ax= b). If one...

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n= 4, c = 7 %3! P4(x) ...

A: Given:       fx=lnx, n=4, c=7   A taylor series is given by               fx=∑k=0nfkck!x-ck here n=4...

Q: e the definition of error function, prove that %3D

A: Topic:- application of integration

Q: A curve has an equation of y = x - 6x2 + 9x + 2. Find the point of inflection of the curve. O a. (1,...

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Q: Find the sum of the convergent series. 6 0.6 +0.06 + 0.006 +. .

A: Given,Sn = 6 + 0.6 + 0.06 + 0.006 + 0.0006 + ..... = 6.66666...    110 Sn = 66.66666....            ...

Q: Find fy for f(x, y) = (In x) (sin x² y). O fy = (In x)(cos x²y)(2xy) O fy = (cos x2y)(x²) O fy = (In...

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Q: Find the derivative of the function. -7 а) у — (2t – 3)2

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Q: In (sin2x) sin2xdx sin3x +C 3 A sin2x +C B sinx +C sin x +C E None

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Q: A piston is seated at the top of a cylindrical chamber with radius 7 cm when it starts moving into t...

A: This is application of derivative problem

Q: Evaluate the following integral. 18x2 dx 2 x* - 41x + 400

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Q: d²y dx2 + 4 + 5y = 2e-2", y(0) = 1, y' (0) = -2 dx

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Q: Show that the differential equation ry'+x(1+y')y = 0 is not exact, but becomes exact when multiplied...

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Q: 7. If y 6e5, then y' = 30e*. The derivative of a product will never be equal to the product of deriv...

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Q: n of eY dydx ? 0.

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Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

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Q: 5. Let f(x, y) = 3xr² + xy- y. (a) Compute f(1.02, 1.99) exactly. (b) Let f(1.02, 1.99) = f(1+0.02, ...

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Q: An spider colony is counted every month. The first three counts are 30,00o, 33,000 and 36,300. Assum...

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Q: Solve the system of linear equations given below. —В — С + 4D %3D 1.8 4А — В — С — 0.5 -A + 4B – D =...

A: Given information -------------------------------------------------------------------------------- ...

Q: Calculate the outward flux F*n ds where F = (x^3, y^3) and C is the boundary of the region x^2 + y^2...

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Q: Find y' and simplify: y = cot(tan x³) - %3D -3x²sec? x 13 y' = 1+tan?x3 %3D X. 3x2sec? x3 y' = 1+tan...

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Q: Find the general solution of the following Differenti 1. y(y2 + 1)dx + x(y² – 1)dy = 0

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)...

A: Given that fx=x+5cosx    x∈0,2πTo find : point of inflectionSolution:if find point of inflection the...

Q: Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, tsin ...

A: To sketch: The curve r(t)→=<tcost,t,tsint> Solution: Given x=tcost,y=t,z=tsint x2+z2=tcost2+ts...

Q: What is the center and radius of the sphere that has (1, -2, 2) and (3, 4, -12) as endpoints of a di...

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Q: Nx - M, If R, where R is a function depending only on the quantity z = xy, then the differential equ...

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Q: kt ek kdt, where k is constant k A) True B False

A: