Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, + (y+ R)u, = R+u? %3D

Q: by implicit differentiation. dx Find 3xeY + ye = 4

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Q: 18) Find a + b, 2a + 3b, |a|,  and |a - b|.  a = 2i - 4j + 4k, b = 2j - k

A: The objective is to Find a + b, 2a + 3b, |a|, and |a - b|.

Q: b a

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Q: Calculus the producer surplus for the supply function p(x) = 3+0.01x at the sales level X = 10. Show...

A: Find your answer below 

Q: P = xi + yj +zk Q = x²i -z²k R = xy²j – yzk PROVE THAT (QX R) *(dot) P = R *(dot) (P X Q)

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Q: To start a new business Beth deposits $1000 at the end of each period in an account that pays 9%, co...

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Q: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2x). (Enter your answe...

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

Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary e...

Q: Calculate the area of the shaded region in the given figure y y=x 2p

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

Q: A. Solve the following problems. 1.) A rectangular plate 12 ft long and 8 ft wide is submerged verti...

A: Here, note that pressure on the surface of a submerged body can be given by: P=ρgy

Q: FIND THE LIMIT USING SQUEEZE THEOREM. SHOW SOLUTIONS. sin x limy→o\

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Q: HOMEWORK LG Solve the given initial-value problems. 4.43. xe* dx + (y - 1)dy 0; y(0) =0 4.44. y(3) =...

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Q: A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 125 feet of fenc...

A: Total fencing available is 125 feet.

Q: Explain why the function is differentiable at the given point. 4x f(x, y) = y + sin (0, 6) The parti...

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Q: 9) A function that is continuous at x = c must be differentiable at x =c. 10) A function that is di...

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Q: 1. Find 2(3z + 4)² dz.

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Q: The top and bottom margins of a poster_are 6 cm and the side margins are 4 cm. If the area of the pr...

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Q: The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is 25 yd long b...

A: It is given that,   1 yard = 3 feet Length = 25 yd = 75 ft Width = 14 yd =42 ft Depth = 5 yd = 15 ft...

Q: Find dy/dx by implicit differentiation cos(x) sin(y) = x2 − 3y

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

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Q: Evaluate log, 99

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

Q: X-9 At what x- values is f(x) not differentiable?

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Q: Let A E R²x2 be special orthogonal. Show that there exists & E [0,27t) such that COS O - sin o A = s...

A: According to question,Given Matrix,A = cos ϑ-sin ϑsin ϑcos ϑ

Q: Directions: Find the limit of the following. 1. lim(x² + 2x – 1) x→2 2. lim (x³ + 8) X--2

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Q: Define the hyperbolic functions as follows. e" - e e" + e sinh r .cosh a 2 sinh x and tanh a cosh x ...

A: We have to solve both Questions.

Q: dy 3) (x+ 1)(y- 1) dx

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the remain...

Q: ry" +xy'-4y 2r y"-2y' +y -3-x+x. y(0) =-2, y(0) 1.

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Q: n one of the warehouses of a construction firm, cement is being released from an elevated storage bi...

A: Volume of cone=13πr2hRatio of diameter and height is 1:1Dh=11h=DVolume of cone=13πD22DV=112πD3 ...(1...

Q: x2ex b. Evaluate lim by using T.E. X-0 CoSX-1

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into ...

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Q: If x2 + y? = 169 and dy/dt = 5, find dx/dt when y = 12. (Enter your answers as a comma-separated lis...

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Q: Find an equation of the tangent to the curve given by x = t* +1, y = t° +t at the point correspondin...

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Q: Evaluate the following integral using partial fractions: x - 1 dx x3 + 2x2 – x- 2

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Q: what is the derivative of hcx) at x =D0 where h lx) =2f(6)-2-VFIR) where %3D

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Q: Iff (x) is a polynomial with real coefficients and zeros of 4 (multiplicity 3), -5 (multiplicity 1),...

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x1, x2) = x +x subject to the c...

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Q: x =r' +1, y=r -1 d'y b) Find dx?

A: Given:  x=t3+1,y=t2-t To find: d2ydx2

Q: 9) In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. ...

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Q: The line segment x = p - y,0 <y < p, is revolved about the y-axis to generate the cone as shown in t...

A: Use simple integration formula for lateral surface area.

Q: Assessment 1. Directions: Find the limit of the following. 8x+1 5. lim X-1 x+3

A: We know by definition of limit for a function f(x) , limx→af(x)=f(a) , provided f(a) exists.

Q: In one of the warehouses of a construction firm, cement is being released from an elevated storage b...

A: Given: Cement is being released from an elevated storage bin at a rate of 29 feet3/min. i.e. dVdt=29...

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(2, 8...

A: Formula to find directional derivative of the function F at a point P(x,y,z) in the of a unit vector...

Q: Find the volume of the solid obtained by rotating the region bounded by y = x - x and y = 0 about th...

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Q: 15–18 Find the angle between the vectors. (First find an exact expression and then approximate to th...

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Q: Σ sin cos(n) п

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

A: To find out the parametric equation and symmetric equation of the line. 

Q: Let a. b, and c be three-dimensional vectors. Identify whether the expression a- (b x c) will result...

A: We can solve this as follows:

Q: Calculate the values of the following serics. 4+ 2" a ) Σ b) (-2)" 3n en n=0 n=1 Hint: write it as a...

A: Given: a)∑n=0∞4+2n3nb)∑n=1∞(-2)nen

Q: 6. DETAILS BERRAPCALC7 3.6.025. 0/2 Submissions Used For the equation, find dy/dx evaluated at the g...

A: We will find the implicit differentiation at a point. 

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

A: We have to find the critical point