Let r(t) (4t+2, -4e¹, 2e #¹). Find the line (L) tangent to r(t) at t = 3. L: (x, y, z) = = +t

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A: If y=f(u) and u=g(x) then dydx = f'(g(x))g'(x) .

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A: Topic - first and second derivative of a function We are given,  y=x5ln(x)we know…

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A: The given differential equation is: y''+36y=e-t Boundary conditions are: y0=y0  ,y'0=y'0yt→0  as t→∞

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Q: PROBLEM - Standard form x+5x11 =y Vertex form Axis of symmetry Opening (upward or downward) Type of…

A: Vertex form of the prabola : y =ax-h2+k ; where (h,k) is the vertex of the parabola .

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Q: Optimal Chapter-Flight Fare  If exactly 196 people sign up for a charter flight, Leisure World…

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Q: 2. Find the speed of the object traveling along the curve r(t) = (t², sin(3t), cos(3t)) time t = 3.…

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Q: D(x) = (x-8)², S(x) = x²

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Q: 4. What is the length of the latus rectum of an ellipse with equation x² + 4y² - 2x - 8y + 1 = 0?

A: Topic = Ellipse As per guidelines , At a time only one question can be answered. please repost for…

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A: Given information (a):-   ∑i=1n f(x1),     (b):-  ∑i=1n f(xi), (c):- ∑i=0n xi ,           (d):-…

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A: I am attaching image so that you understand each and every step.

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Q: explain in your own words how the definite integral can be used to determine at least 2 different…

A: Please see the below picture for detailed solution.

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Q: Which of the following is the simplified expression of 1- 1 sece sin²e cos²0 O tan²e O sec²9 cose?

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Q: 1 √₁2²-4 d x² - 4

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Q: Evaluate

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Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: 200 2. Evaluate: 22oo(2x – 5)2

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Q: Describe the domain and range of the function. f(x, y) = 9x² - y Domain: {(x, y): x ≥ 0, y ≥ 0} {(x,…

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Q: radius of a sphere increases at a rate of 7 centimeters per second. Find the radius of the sphere…

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Q: A rational fraction of the form g(x) = 0. Select one: O True O False f(x) is called a proper…

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Q: Find the values of the following limits. If a limit does not exist, type DNE in the entry box. 2x³ +…

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Q: lim-→-1 O 0 0-2 0 - 12/1 x²+3-2 x+1 O None of the above =

A: To evaluate the following limit.limx→-1 x2+3-2x+1

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Q: If g(x) = 5 +x+2e², find g-¹(7) = 1

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