Find the unit tangent vector to the curve at the specified value of the paramet r(t) = t³i + 3t²j, t = 3

Q: Find the indefinite integral and check the results by differentiation S(4x²+ + 3)²dx

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Q: SX7UPET dx

A: I=∫x7x4+1dxI=∫x4(x4+1)x3dxI=14∫x4(x4+1)4x3dxSubstitute x4+1=u

Q: 1. The general solution of the system [x' = y, y' is given by x(t) = C₁ cost + C₂ sint, y(t) = C₁…

A: x'= y..........(1)y'= -x.........(2)

Q: Find the limit of the sequence: 5n²+8n+3 3n² + 8n +7 an

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Q: Let g(z) = 6 Determine the most general indefinite integral of g. 1 6dz

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Q: 8. Use the method of substitution to evaluate each of the following general antiderivatives 6x² (a)…

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Q: = Find fæ, fy, fxx, fyy, fay for the function f 5 x³ siny+8 y² cosx+3x+7y.

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Q: The Taylor series for f(x) = x³ at-4 is cn(x + 4)". Find the first few coefficients. Co= C1 = C2 -…

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Q: (t²-2t)³ 5t 4. The voltage applied to a 0.25-F capacitor is given by v=- 3.7 s. . Find the current…

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Q: x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x…

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Q: Find T 1 = -1 wwwman x² dx + C

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Q: (3√2, -3√2,6) to cylindrical to cylindrical coordinates. Enter your answer as an ordered triple and…

A: Cartesian coordinates:(x,y,z)=(3√2,-3√2,6)

Q: What are the coordinates of the vertex of the equation (+8)² (x+2)² 36 = 1? 25 O (-2,-2), (-2, 14) O…

A: The given equation is

Q: 2. Evaluate the integrals. a. b. C. L (6x - e²) dx [²₁12 +2 (2 + 2y)² dy 7T/4 3 3 sec Ꮎ tan Ꮎ ᏧᎾ

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Q: The Taylor series for f(x)=x³ at 3 is Σen(x-3)". Find the first few coefficients. Co C1 C2 C3 C4 =…

A: The given function is The Taylor series

Q: 9. The angular displacement of a spinning shaft is given as = 0.7t² - 5t+3, where is in radians and…

A: Given that the angular displacement of spinning shaft is where  is in radians and t is in seconds

Q: please i dont understand that you did after step 3 from 0=sin(2pi c)

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Q: 3. The behavior of the system is a spiral source. x' = y' = = 3x + y, -x + 4y

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Q: lim У-у-г уг -30+2 зу Уже

A: We have to findlimx→−2

Q: Find an upper bound on the error that can result if cos(x) is approximated by 1 - (x²/2!) + (x^/4!)…

A: Here we have to find an upper bound on the error that can result if cos(x) is approximated by  over…

Q: Considering the interval [−2, 4], does the Mean Value Theorem for integrals hold for f (x) whose…

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Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: The system of differential equations : has the solution Y C₁ et V₁+ C₂ e¹₂ V₂ + C3 e¹³ V3 where (in…

A: Given that

Q: Given the function f(x) = 5x² − 3x + 9 and the point P(-4, 101), which lies on the graph of f(x),…

A: The objective of this question is to find the equation of the tangent line to the function f(x) =…

Q: The function C(t)=C0(1+r)t models the rise in the cost of a product that has a cost of C0 today,…

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Q: You have to examine the relationship between the age and price for used cars sold in the last year…

A: From the above table we…

Q: Specify the period and amplitude for the function. period amplitude -20 -15 -10 -5 11111111 y…

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Q: Given the geometric sequence: 20 3 find a formula for the n-th term: ao = 2, a₁ a1 = , a2 = 200 9…

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Q: 4. Evaluate the integrals. a. b. C. Lou + 3 du +3 6². v³ +3v4 v² √2/43 -dv π/4 3 +7 (cos (0))² (cos…

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Q: Consider the following parametric curve. Answer parts a and b. 70 x=2 sint, y = 2 cost; t=2 a.…

A: The given parametric equation of curve is

Q: Find all intervals on which the function f(x) = (x² − 3) e-ª is decreasing.

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Q: If f is continuous and f(x) dx = 12, find So f(2x) dx.

A: Given that To find

Q: Find the second derivative of the following functions: a. f(x) = x5 + sin x b. f(x) = x² + == x c.…

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Q: f(x) = (5z – 3)(4: 6(2-0³) 3-20 f(9) = 3 ၁၂ နှ

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Q: Find the mass of a lamina bounded by y=5√x,x=9,and y=0 with the density function σ(x,y)=x+1

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Q: 3/4 Find the cost function if the marginal cost function is given by C'(x) = x C(x) = +5 and 16…

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Q: 4x (11 + x) Find the first few coefficients. Suppose that CO C1 = C2 = C3 = C4= ∞ n=0 Cnx". Find the…

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Q: Σ(17)

A: ∑n=1∞(3n+7n11n)

Q: Find parametric equations that describe the circular path of the following person. Assume (x,y)…

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Q: 7. Linear Algebra - Linear Equations 2 Which of the following statements is true about the solution…

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Q: Find an equation of the line tangent to the following curve at the given point. 2 5x 3' 6 y = T= 1…

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Q: This problem finds the derivative of a function using the formal definition. The process is broken…

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Q: Find a simplified series representation of x²e4 answer = n

A: The given function is x2e4x.

Q: 3. Two savings account start with $100 each. Account A earns $2 annually while account B earns 2%…

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Q: 61. Presale Order A wireless store owner takes presale orders for a new smartphone and tablet. He…

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: Here

Q: A company has found that the cost, in dollars per pound, of the coffee it roasts is related to…

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Q: 1. Use the Limit Comparison Test to determine whether the series below converges or diverges. List…

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Q: Find the Maclaurin series of e 00 1 0

A: The given function

Q: Suppose that the radius of convergence of the power series   cn xn is R.     What is the radius of…

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