Find the directional derivative of the function at P in the direction of v. V2 f(x, y) = x³ – y³, P(4, 3), v = (i + j) 2 %3D

Q: ue Q(t) = 2400e-0.05t where t is measured in years, answer the following questions. (a) What is the ...

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Q: Determine the general equation of the plane satisfying the given conditions: plane A containing the...

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Q: - partial fraction 1 -dx x(x² +1}

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Q: (x – 3)2 (y – 2)? = 1 - Given the ellipse 16 36 Find the center point: List the two major vertices (...

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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: 9. (2y2 + 2y + 4x?)dx + (2xy + x)dy = 0; when x=-1 and y=0 %3D 10 v-5du -4dy -vdy. hon vー

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Q: Evaluate. S*+ 2y)dx dy 3.

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Q: Write a differential equation that models the given situation. The stated rate of change is with res...

A: Find your answer below 

Q: A. Write the missing term/s in the given series of numbers. 1. Find the next three terms in: -14 -10...

A: 1.      -14,-10,-6,-2,_,_,_ -14+4=-10-10+4=-  6    -6+4=-  2   -2+4=      2        2+4=      6      ...

Q: Let D be the trapezoidal region in the ry-plane bounded by the graphs of z = 0, y = 1, y = z and y =...

A: We have to solve for the area by integration. 

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: 2. Integrating factor by inspection: Solve the equation: (y – xy²) dx + (x + x?y²) dy = 0 O = In y –...

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Q: 2. For the following complex numbers; peform the indicated operations. Expressresultsin rectangular ...

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

Q: Let f(x, y) = xy – y + cos x. af Find (a) fe dy and (c) the mixed partial fæy. (b) O (a) xy - y (b) ...

A: Find your answer below 

Q: Find the area of the region that hosmside the Circle r = 3COS 6 and outside the cardioid r =1+ cos 0...

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin(/2t), y(0) = 14,...

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Q: Determine whether each point lies on the line. x = -1 + t, y = 2t, z = 3 + t (a) (0, 2, 4) O Yes O N...

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Q: piece of wire 26 m long is cut into two pieces. One piece is bent into a square and the other is ben...

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Q: - partial fraction 1 dx x(x² +1}

A: Let's find. 

Q: 3. Graph the system of inequalities. y 2x-3 y>x+1

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Q: olve the bessel equatio

A: answer of given question is in step 2

Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 3y = 0, y(0) = 1, y'(...

A: We have to solve above Laplace transformation 

Q: E2-3

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Q: (cos x+xcost)dt + (sin t-t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: y = ² + 3 in the Cartesian form y t Express the parametric f(x). curve x t+7

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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 the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in...

A: Question- Find the point of diminishing returns (x.y) for the function R(x) , where R(x) represents ...

Q: y = sin x ,x = 0, y = 1; about y = 1. %3D

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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: dx (p) x² + 25

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Find the Taylor polynomial T(x) for the function f centered at the number a. f(x) = x + e-x, a = 0 T...

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Q: The region bounded by the curve ×=y2, the y-axis, and the line y=2 is revolved about the x-axis. Fin...

A: We have to find volume. 

Q: 11. An airplane is flying parallel to the ground at an altıtude of 2 km and at a speed of 4 km/min. ...

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Q: 1. e (3xy-x)dx+e* dy = 0; when x = 0, y = -1 4 Ans. y =-- 1 3

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Q: Fill in the missing numbers in the table below. Then use the table to fill in the apparent value of ...

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Q: Approximate the sum of the series correct to within 0.00001. (-1)" n= 1

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Q: 6. (Sections 8.8 and 8.9) Determine whether the following piecewise-defined function is a probabilit...

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Q: A spherical snowball is being made so that its volume is increasing at the rate of 8ft^3 min/ Find t...

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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: the edge of a tablecloth. The fringe comes in 5. Leslie needs 324 inches of fringe to put around of ...

A: one jar make 26  so 4 jar make = 26*4 = 104 cup    1 yard = 36 inch 10 yard = 360 inch leslie requir...

Q: A function f(x) and interval [a, b] are given. Check if Rolle's Theorem can be applied to f on [a, b...

A: To test whether Rolle's theorem is applicable or not.

Q: (s + 1)3 s6

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Q: (b) Oppositely directed to 9i – 6j + 3k. - (c) Same direction as the vector from the point A(-2,0, 2...

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Q: f(x) = (3x + 1)(x – 4) / (x + 2)(x – 2) %3D Domain x-int = Intercepts y-int = V.A. Asymptotes and Ho...

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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: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

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Q: Use differentials and the graph of f to approximate the following. (Round your answers to two decima...

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Q: 12. Exact equations: Solve: 3xy²dx + (3x²y + 4y²) dy = 0 O ry + y* = c O r?y² + y* = c

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as ...

A: ANSWER IS GIVEN BELOW.

Q: Jse cylindrical coordinates to calculate fSfw f(x, y, z) dV for the given function and region: f(r, ...

A: We need to evaluate integral using cylindrical coordinates.