(i) re dr -2

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

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Q: der the following planes. 5x + 2y – z = 44 x – 4y + 2z = 0 (a) Find the angle between the two…

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Q: Note: you will need to find both the gener e homogeneous problem, and a particular so mogeneous…

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Q: Find the following limit by evaluating an appropriate definite integral over the interval [0, 1 lim…

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Q: 5(3х-1) dx sec ( 3x²-2x)

A: On doing integration we will get

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Q: Which of the following is not equivalent to cos(0 + 0)? cos 8 cos 0- sin 60 sin 0 1- 2 sin? 0 O…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: Solve the given initial-value problems. te dx +(y-1)dy=0; y(0) 0 4.43.

A: identify the differential equation and solve it.

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

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Q: Consider the following. u = 5i - j - k, v = -i + 5j + 2k (a) Find the projection of u onto v. (b)…

A: The expression for the vector projection of u onto v is: projvu=u·vv2v And The expression for the…

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: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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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: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Solve the initial value problem. dv 8 t> 1, v(2) = 0 dt

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: A detailed solution is given below

Q: Find a point Pon the line and a vector v parallel to the line by inspection. Enter the vector ias i…

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Q: 2. Solve the given the equation using the integrating factors found by inspection. [2х + усos(ху)jdx…

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Q: 1. (3x²+ 2y²)dx + 2xydy=0 2. (x- 3y + 3)dx + (3x + y + 9)dy = 0

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 4. у %3D a sin(2x + 3)

A: To form the differential equation for the given function.

Q: A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled…

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

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Q: ds Find the function s(t) satisfying = 4 -9 cos t and s(0) = 7. dt

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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: 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 for the following equation: y''' + 3y'' – 4y' – 12y = 0

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

Q: EVAUATE FL) OF TRE DIFF ERENTIAL EQUATION AT zEto NITI AL CONDITONE. oit

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: use the definition  of exact or non exact.

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: Find the dot product of the following vectors u and v. %3D

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Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: An ice cream cone is filled with ice cream and surmounted ice cream in the formof a hemisphere on…

A: Given problem:- An ice cream cone is filled with ice cream and surmounted ice cream in the form of a…

Q: 2x

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Q: Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j…

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Q: The two sides of a triangle are of lengths 300m and 150m, and the angle opposite the 150m-side is 26…

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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: (b) If a > b and c > 0, then ac > bc.

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Solve the given initial-value problems. 4.43. re dr +(y-)dy 0; y(0) 0

A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

Q: find the inverse laplace tramsform 3/(s-2)^2+4

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Which of the following is equivalent to cos 0-2 cos 0 sine 1-sin 0+sin²0-cos²0° tan 0 cot 0 O Option…

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