Let C be the curve y = 5x for 0

Q: За + 5; у 3 3а — 1; Let R be the region bounded by the straight lines y y = 10 – 4x; y = 8 – 4x. Con...

A: We have to sketch Region R and Reigon G

Q: (1-x²)-1/2 Arcsin x

A: We will integrate the given function using simple Integration method.

Q: cos x dx Sx x sinx cosx dx 4. 3.

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Q: Find a set of parametric equations for the line passing through the point (4, 0, 7) that is parallel...

A: topic - equation of a line

Q: Find the derivative of the function. f(x) = 7x2 In(9x)

A: To find derivative of given function.

Q: Exact equations: Solve * (2x + 3y) dx + (3x + y - 1) dy = 0 O x* + 6xy + y² – 2y = c O y2 + y* = c

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 - x + + 3y + z = 7 2 Find the normal vec...

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Q: By applying Rolle's theorem, check whether it is possible that the function f(x) = a° + x – 6 has tw...

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ Vt, y = et at the p...

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Q: 4. Find the general solution of the differential equation using the method of undetermined coefficie...

A: Let's find. 

Q: cos x х dx /sin x COS

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Q: If f'(x) and g'(x) exist and f'(æ) > g'(x) for all real æ, then the graph of y = f(x) and the graph ...

A: f'(x) and g'(x) show the slope of function  so here given that slope  f(x) > g(x) so they do not ...

Q: h as suggested by the equ )dx +3(x+ 2y)dy = 0 whem

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Q: 4. find the absolute max. and min. of the function f Plate boun ded by = x? +y2 on the closed triang...

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Q: %3D

A: Find the second derivative and substitute in the given differential equation and solve for r. 

Q: The region bounded by the curve x=y?, the y-axis, and the line y=2 is revolved about the x-axis. Fin...

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Q: Find the indefinite integral. (Remember the constant of integration.) (0.9t2 + 0.08t + 9) dt

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Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v ort...

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Q: Solve the following: a) [4/(x+ 1)] – [2 / (2x – 1) b) (1/y)+(1/2y)+ (2/3y) c) (2a²b³/3z²)÷ (ab²/2z) ...

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Q: 10. Homogeneous Equations: Solve the differential equation: xdy – ydx – x? –- y²dx = 0 O arccos() = ...

A: dydx=y+x2-y2xdydx=yx+1-(yx)2y=vxdydx=v+xdvdxv+xdvdx=v+1-v2x dvdx=1-v2  ...(1)

Q: Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 = ...

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Q: A stone is dropped into a still pond. Concentric circular ripples spread out, and the radius of the ...

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Q: Find the point on the line y = 2x + 5 closest to the point (6, 1). The function giving the distance ...

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Q: Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

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Q: Q3: Solve the following first order differential equations Use any method: dy 1-2у-4х dx 1+y+2x

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Q: 1. D + The region D above lies between the two red lines and the red parabola y ?. It can be describ...

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Q: Consider the following. u = -7i – 4j – 2k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find...

A: Here, the given vectors are: u=-7i-4j-2k, v=0i+4j+4k That is: u=-7,-4,-2, v=0,4,4

Q: Evaluate the following integral over the Region D. (Answer accurate to 2 decimal places). I 5( . sin...

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Q: ydx -(x +3y)dy = 0 Ans. x = 6y In

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Q: 4. What is the equation of the normal line to the curve 4x2 – 9y2 = 1 at point (3,2) ? a. y =x- 4 5....

A: Slope of the Normal Line to the graph of f(x) is  -1f'(x). Equation of the line : y-y1=mx-x1 where, ...

Q: Q1: Find the solution of the following Differential Equations d²y 1. + y = 6e* + 6 cos(x) dx2 d?y 2....

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Q: Linear coefficients in 2 variables: Solve the equation: x – y + 1) dx – (x + 4y + 1) dy = 0 O In[(x ...

A: Solution of the problem as follows

Q: 수) +sin?y-0 2 (fy) dx dx

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Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+2k w = i+ 9j + 2k Find the v...

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Q: -2 sin x where y () = 7 dx O y = 2 cos x + C O y = -2 cos x + C

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Q: 7.75 and has a focus at Write the equation of a parabola whose directrix is x (8.25, 6).

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Q: A lamina with constant density p(x, y) = 6p occupies the given region. Find the moments of inertia I...

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Q: Let f(x, y) = x² + xsin(y). %3D

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Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price...

Q: Integral of 2xln(1+x)

A: We will solve the integral. 

Q: the following. (x) = x? %3D + 6x + 7 Find the critical numbers. (Enter your answers as a comma-separ...

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Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) y = ...

A: We have to solve above derivative 

Q: Which one of the following is the vector equation of a plane containing the points: (4, 0, 3), (1, –...

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Q: 5. Check if the following is a separable equation. dy * = xy + 1 O variable separable O not variable...

A: The detailed solution is given below Thanks 

Q: 2. For the following complex numbers; perform the indicated operations. Expressresults in rectangula...

A: Given: za=-2-5izb=2.15e4.18izc=1.75cos165°+isin165°zd=0.745∠-36°ze=1+3izf=0.953cos324°+isin324°zg=2....

Q: Profits at The Christmas Store vary periodically with a high of $50,000 in December and a low of $10...

A: Explained below 

Q: 15. f(x) = for every x E (-4,3] x+4 16. f(x) = sin (2) in the interval x 2-2 3 17. f(x) = { 2 - x2 i...

A: As per our guide lines we are advised to solve only first question. Please kindly upload other quest...

Q: Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of...

A: One of the foci            =0,0    poleeccentricity                   = 4vertex nearest to pole = 2,...

Q: Find the area of the triangle with vertices P(1, 5, –4), Q(0,0,0) and R(2,4, 1). NOTE: Enter the exa...

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Q: Determine whether each point lies on the line. x = -3 + t, y = 6t, z = 5 +t (a) (0, 18, 8) O Yes O N...

A: Line in 3D