Determine if the following functions are continuous on the interval I. (i) f(x) = -x. (0, 1) I 2 x-x

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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: 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 Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize...

A: Let's find. 

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = V x? + y? + z? (5,...

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Q: Construct the table of signs for f'(x) and f"(x) ginve f(x)= x4ex on its domain of (-inf, +inf)

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Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

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Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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Q: 6. Using L' Hopital's Rule, find the value of the limit L- lim +1

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

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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: 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: satisfying

A: We will obtain the particular solution. 

Q: 4. Determination of Integrating Factors: Solve the equation y (4x + y) dx – 2 (x² - y) dy = 0 O 2r? ...

A: Given

Q: We now use the substitution u = x° + 8x and du = (9x8 + 8) dx to convert the entire integral into on...

A: Given the integral  ∫9x8 + 8x9 + 8x2 dx We now use the substitution  u=x9+8x and du=9x8+8 dx.

Q: Determine whether each of the fo for convergence/divergence. (a) n +1

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

Q: 13.Exact equations: Solve: (2r3 + 3y) dx + (3x + y – 1) dy = 0 O x* + 6xy + y² – 2y = c O r?y² + y* ...

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Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x) =-+...

A: Solve differentiate

Q: Integrating factors y(x^2 + y ^2 − 1)dx + x(x ^2 + y^2 + 1)dy = 0 when y(1) = 0

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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: (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: 4. Determination of Integrating Factors: Solve the equation y (4x + y) dx – 2 (x² – y) dy = 0 O 2r? ...

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Q: Evaluate the following series two ways: 4 4 3k k=1 3k+1 (a) Using a telescoping series argument. (b)...

A: Given that ∑k=1∞ 43k-43k+1a.431-432+432-433+433-434+434-435+......+43k-43k+1=431-43k+1=431-43∞+1=43

Q: (ysin x+xy cos x)dx+(xsin x +1)dy = 0 Ans. xy sin x+y = c

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x

Q: Let X be a random variable with p.d.f f(x) = 2x,0 < x < 1. Find E(Vx). 2/3 5/4 3/2 4/5

A: Given

Q: cotx dx In|csc x| cSC

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Q: Find for F(X,)= Sin xy+ T Y²-x = 0

A: Given query is to find the derivative of the expression.

Q: Homogeneous function: Determine the homogeneity of the following functions. x³ - xy + y homogeneous ...

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Q: a) lim x-3 x+1 x2 – 4x + 4 b) lim x-2 x2 +x - 6 y? – 4y – 21 c) lim y-7 3y2 – 17y – 28 t3 +t2 – 5t +...

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant an...

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: 4. f(t) = V3 – 2t , find f""(t) %3D

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Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

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Q: 2. Find the general solution of the differential equation: dy ip 5 + 6y = e ,3x - dx? d.x

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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: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

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Q: Evaluate the following integrals: 1. S (3* + 4°)² dæ

A: We can find the integration as below

Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: dy -2 sin x where y (5 = JT dx

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below 

Q: 2. Find a particular solution to each of these ODES by using the method of variation of parameters: ...

A: Note: as per our guidelines we have to solve 1st question. So please repost other questiin . sorry f...

Q: y = a sin (x + b) u sin (x + b) -a sin (x + b) O a cos (x + b) O -a cos (x + b)

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Q: Find the area of the triangle with vertices P(1, 4, –6), Q(0,0, 0) and R(3, 4, 1). NOTE: Enter the e...

A: topic - area of triangle

Q: (s + 1)3 s6

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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

Q: (t -x)dt – tdx =0; when t = 1, x = 5

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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: Ду dy %3D II

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