3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) = (t3 – 2t, t3 + 2t), 0

Q: 11. If f"(x)=-4sin 2.x, f(0)=0and f'(0) =2, find the value of f 4 %3D

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Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: [3 Compute the matrix exponential e4t for the diagonal matrix A =

A: Given,  A=3004

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A:

Q: 5. If x = 5cis(2.945)and y = cis( – 0.755) find xy³. Leave your answer in polar form. Note the…

A: If x=5 cis2.945 and y=cis-0.755, then to find xy3.

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A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

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A: We have to draw the root locus curve.

Q: Calculus Question

A: To simplify the given rational expressions.

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A: The curve y=19x3 from 0≤x≤2 revolved about x-axis.

Q: nswer.

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A:

Q: 3. a) If 2 - i is a root of x³ – 2x² – 3x + 10 = 0, find the other complex root. b) Calculate the…

A:

Q: (a) Determine the Cartesian equation for the parametric curve defined by x(t) = 5 sin t and y(t) =…

A: We have to find the equation of the curve ,tangent equation to the curve.   Note - As per our…

Q: Example: Find C² sint]? Solution:

A: To solve the following problem

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A:

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Q: Find the particular solution of the following ODE given that y(0)=7 and y'(0)=0: d’y dy dx -+3-10y=0…

A: To find the particular solution of ode

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A: Explanation of the answer is as follows

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A: Substitution is done for the function whose derivative is present in the numerator.

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Q: r the function. (Center your power series r - (Enter vour a nswer using interval notatio

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Q: 6. Find the intervals on [0,2r)where f(0) = sin²(0) is concave upward/ concave downw %3D

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Q: cos e d0 Jo 1+sin? A 2

A:

Q: Find the graph of the equation 4x 2 + y 2 = 4.

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Q: Evaluate the limit sin 9x lim I0 sin 3x

A:

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A: The given triangle is:

Q: Evaluate the indefinite integral. Sa V1 – x? daæ - cos° 0 – cos' 0 +C } (1 – a²)%/2 – }(1 – 2²)/² +…

A:

Q: From Rogawski ET 2e section 10.5, exercise 7. Apply the Ratio Test to determine convergence or…

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Q: Solve the system of equations. x+2y = 0 8y = - 4x Solve the first equation for x. x +2y = 0 x = y

A: x+2y = 0 8y = -4x 2y = -x put this in equation  so the the equation has infinite solution    x + 2y…

Q: certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 59 - 2.2t…

A: Given query is to find the average temperature for the given time interval.

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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Q: Integrals

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Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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Q: Q1/0fin t the Tulorssevies at- for F(): Sinメ Iat ○ F(対 ak y=1 f(x) =

A:

Q: The demand curve for a certain product is given by p(q) = 541 - q. The supply curve is given by p(q)…

A:

Q: 13. Explain in your own words what a limit is. Use several diagrams and be sure to consider lim…

A: This is a problem of limit. Based on the general formula we will answer the question.

Q: Given 1 2 3 0 14 X y 5 6 0 W Find the value of "w". NOTE: Just give the answer for w. Answer:

A:

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A: We have to find the volume of the object.

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Q: 72n+1 E(-1)" 22n+1 (2n + 1)! n=0

A: Explanation of the answer is as follows

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A: Given query is to interpret the marginal cost C′(25) = 4.

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A: Given,  dydx=2e-2x and y(1)=4

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

A:

Q: Find an equation of the plane. The plane through the point (7, 8, 1) and with normal vector 3i +j -…

A: