I) Consider the function: y = + C,e2x + C,e-5x + Czxe-5x

Q: Solve the following system of IVP: -3 3 x' = Ax where A =-2 -1 1 and x(0) 21 %3D 3.

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Q: Write the equation of a sine or cosine function to describe the graph. y 4- 3+ 2- 2n 10n -1 3 -2 -3

A: The equation of a sinusoidal wave is given by:y=p(sin(q(x+r))+dwhere p=amplitude, q=2πperiod,…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 2 and f'(0)…

A: We need to find f(5).

Q: dx Evaluate: xV x² + 4 None of the given choices +4 - 4 + C 1 4 V x< +4 + 4 x² +4 – 4 + C x<+4 +4 x²…

A: integration

Q: Find Duf at P. f(x, y) = sin(6x – 4y); P(4, 6); 4 3 i u = j JOTE: Enter the exact answer. Duf =

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Q: Using a model of the prototype ball thrower, a ball is fired into the air with an initial upward…

A: Given that height of the ballht=-16t2+48t+41.if balls reaches maximum height then…

Q: (b) x = 5+ 7ty = - 3+ 10t, z = 6 – 4t O (x, y, z) = (5, 3, 6) + t(7, 10, 4) ai + bj + ck = (5i + 3j…

A: Given that x=5+7t ,y=-3+10t ,z=6-4tcertisian…

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: Find the area of the given triangle. Round your answer to the nearest tenth. Do not round any…

A: Given:

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 13 15. r(t) = t'i + t5j K(t) =

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Q: Find the vector component of v Enter the exact answers. (4, – 1, 7) along b = (2, 3, -6) and the…

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Q: Determine whether the series is convergent, absolutely convergent, conditionally convergent, or…

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Q: Use the given graph to estimate the value of each derivative.  (a) f ′(−3) (b) f ′(−2) (c) f ′(−1)…

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Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + 2²; P(0,-4, –5);…

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Q: t is known that the total cost function incurred by a company is expressed by C = Q3 - 118Q2 + 2630Q…

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Q: Given the function, y = x' + 3x which of the choices is the correct second step based on the…

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Q: Find the area of the parallelogram that has u =i- 2j + k and V=2j+ k as adjacent sides. NOTE: Enter…

A: Find the area of parallelogram

Q: ain:

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Q: a. Intermediate-Value Theorem from Intermediate-Zero Theorem? D. Right-Hand Continuity from…

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Q: 4. Evaluate: lim (x,y)→(3,2) x cOS TY

A: To evaluate the limit of the given function, substitute x=3 and y=2  in the given function.

Q: By substituting y=xv, solve the given differential equation, (2xy+ x²) dy = 3y² + 2xy with dx the…

A: The given DE is: 2xy+x2dydx=3y2+2xy⇒x22yx+1dydx=3y2+2xy⇒2yx+1dydx=3yx2+2yx⇒dydx=3yx2+2yx2yx+1

Q: Find the maximum product of two positive numbers given that the sum of the first number and twice…

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Q: 4. f(x) = Vx , g(x) = Vx + 1 %3D %3D V4-x2 5. f(x) g(x) = |x| %3D V4-x

A: 4. Given : f(x) = ³√x = (x)1/3 and g(x) = √(x + 1) = (x + 1)1/2 fog = f[g(x)] fog = f[(x + 1)1/2]…

Q: dy The linear differential equation dx 2 has the integrating factor equal to (Note: Simplify or…

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Q: A frameless painting with a size of 2 meters by 2 meters hangs on the side of a wall where its…

A: Solution of the problem as follows

Q: Find the average rate of change of function f graphed below over the interval 4sx s 8. Compare it to…

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Q: 3z-2x² -1 (2z–1)®

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Q: Q6/Find the derivative (df/dx) f(x) =+5 e* %3D -4 x-7/3 + 5e* x-7/3 + 5e* O 1, O 2 Fr73 + 6e"

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Q: S. Elli gives her son Paul 1¢ on his first birthday, 2¢ on his second birthday, 4¢ on his third…

A: Here, the amount doubles on every birthday starting from 1c. That is we have the sequence:…

Q: Find the area of the region that lies inside the curve r =1- sin 0 and outside the curve r = 1.

A: I have provided this answer with full description in step-2.

Q: 3. Find the equation of the tangent plane and the equations of the normal line to the surface z = In…

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Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: Determine the number at which h(x) = V16 – x² is continuous. %3D | Vx2 – 1 Determine the largest…

A: In these question , we can check where the function is continuous . Check where the function is…

Q: Given that Vf (3,-3) = 7i- 6j, find the directional derivative of the functionf at the point (3,-3)…

A: Given query is to find the direction derivative.

Q: t3 after takeoff (where s is in meters), If a rocket travels according to the function s = then its…

A: As per our guidelines we can help you in solving only first problem . Rest of the problems, you have…

Q: Solve for a andb that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: 1) Sketch the curve. a) r=-2 sin O r = -2 sin O Show All Work

A: Explanation of the answer is as follows

Q: particle is moving with the given data. Find the position of the particle. a(t)= 2t+3 , s(0)=4 ,…

A: Given query is to find the position function.

Q: (cos 12t – cos 3t) dt 2 sin7t sin4t dt= A True (B) False

A: This question is based on indefinite integral and Trigonometric equation.

Q: A floodlight is positioned on the ground shining on a white wall 10 m away. A woman 1.6 m tall…

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Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

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Q: a. rdt1.0: sending side

A: Note- I am answering the question as per diagram as further details does not mentioned in your…

Q: tan zdr

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Q: 1 0.5 -5 -4 -3 -2 1 2 f -0.차 -1 -1.5 -2 5. Is the function continuous at x = -3? 6. Is the function…

A: topic - continuity of a function

Q: For the function f(z) = 3x- 2x +2, f(r + h) - f(x) evaluate and simplify: 4: Find the value of the…

A: Here, f(x)=3x2-2x+2

Q: 1. Perform the following integration: S 3sec?x dx - 2x+3 b. а. S(1+) dx с.

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Q: c) Find an equation for the plane parallel to the plane 2x – y + 2z = -4 if the point (3, 2, –1) is…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 2In(sin) de tan() 02

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