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Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

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Q: Given than | f(x) dæ = 4 and f (x) da 8, which of the 3 following is NOT TRUE?

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Q: Funetion Values. Find Re f. and Im fand their values at the given point z. f) = 1/1-2) at 1- i 2) at…

A: Since we have the function                                             fz=11-z then we have to find…

Q: Evaluate ſV7– x²dx

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Q: Find the area bounded by the parabolas y^2 = 4 –x and y^2 = 4 – 4x.

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

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: A solid spherical steel ball, 20 cm in diameter, is placed into a tall vertical cylinder containing…

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Q: The graph of fis shown. Evaluate each integral by interpreting it in terms of areas. y y= fx) 6. 0.…

A: Given query is to find the value of the integral.

Q: e* +e* –x? - 2 Lim sin? x– x? 2

A: To solve the given limit of the function

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Explained below

Q: Solve for the following application of first order differential equations. Show your solutions. 3. A…

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: t/3 cos e sin 20 de T/6

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: Find the second derivative of the function. f(x) = e−4x + e2x

A: Given query is to find the second derivative fi the expression.

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: For what values of x is the graph of y=xe-4x concave down

A: Given  that y=xe-4xSolution :if d2ydx2<0 then concave down.

Q: 2) y TC cos 30 1 b: Period: a: d: Phase Shift: C:

A: We have to find a,b,c,d, period and phase shift.

Q: s e8*(x³ + x²)sec² (x*e3* + 1) dx

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Q: Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

A: Solve the differential equation by assuming eλx for some constant λ.

Q: e length and breadth of the floor of a room are 30 ft. and 20 ft. pectively. Square tiles of 2 ft.…

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Q: x³ dx 9+x* 1.

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Q: -8e4t* + 2e6t cos 2t

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Q: Determine whether each point lies on the line. x = -2 + t, y = 4t, z = 5 + t (a) (0, 8, 7) O Yes No…

A: topic - lines and points

Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: Find Ay and f'(x)Ax for y = f(x) = 6x, x =4, and Ax = 0.06.

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Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y =…

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Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: (4) Consider the function f(r) = r +2- 36r +4. (a) Find the local maximum and minimum values. (b)…

A: As per bartleby guidelines we only give first question answers.

Q: Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) x2 - 36 lim…

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Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x° -…

A: Here we have to factorize the given cubic equation.

Q: Which of the following is NOT a solution to the trigonometric equation sin 0 + cos 0 = 1? O Option 1…

A: Substitute the values given in the options and verify.

Q: Direction: Solve the following equations using separation of variables. 2. y' = x(1+ y²)

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Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

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Q: The shaded region shown below is bounded by the functions f(x) = -3x2 + 8 and g(x) = 0.5x + 6 and…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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Q: If one side of a square is 5 meters in length, what is the length (in meters) of one diagonal? * 5/2…

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Q: PARTA AL FRALT 1ON INTEERALS 2)

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Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: Sx² et* dx 1 e x (8x2 - 4x + 1) + C 16 (8x2 + 4x- 1) + C e4x 16 e4x 32 (8x2-4x + 1) + C e* (8x2 + 4x…

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Q: S cor* (***) csc (*) da 3x+1) 3 3x+1

A: Solution…

Q: An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal…

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Q: 18. lim x+oo 3 20. lim log,

A: Given function f(x)=log12 x we write    log10 x=  log x     and we know thhat    log10 10=1

Q: (x² + y² ) dx – xydy = 0 O 2y = x In cx² O y? = x² In cx²

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Q: sino Given that 0<0 < I 2, what is the exact value of sin(20)? 3 and

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Q: A number is one more than thrice the other number. What is the minimum product of the two numbers?…

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