The slope of the tangent line to f(x) = cos(x) sin(x) at x = ㅠ 2 5

Q: Find the volume of the parallelepiped with one vertex at (1,5, 0), and adjacent vertices at (-6, 12,…

A: Given:     One vertex is  O1,5,0     Adjacent vertices are P-6,12,-4…

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Q: 9. Consider r(t) = (2 cos (t), 2 sin (t), -t). Find the unit tangent, unit normal vectors, T (t), Ñ…

A: We want to find unit tangent vector, unit normal vector and the curvature.

Q: How did you do Step #2, please show detailed steps

A: Step 2

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Q: Find the elementary matrix E₁ such that E₁A = B where 9 10 A = 8 -19 - 20 1 11 E₁ = 010 0 0 1 0 1 -1…

A: Matrix

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Q: Evaluate the limit lim (t + 4)i + 3t²j+e¹k t→0 Enter your answer in i, j, k form.

A: limt→0t+4i→+3t2j→+etk→

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Q: Given the graph of a function f(x), sketch the graph of the derivative on the axes below: f(x)

A: Given: The graph of the function f(x) is given. To find: The graph of the derivative function:…

Q: Consider the following vector function. r(t) = (3t², sin(t) - t cos(t), cos(t) + t sin(t)), t> 0 (a)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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Q: Evaluate the limit. lim X-18 2 + x 3x - √4+x²

A: Given expression, limx→∞2+x3x-4+x2

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Q: Find the domain and range of the function graphed below. Domain: T Range: 3 ردا N 744 -6 -5 -4 -3 -2…

A: need to find out the domain and range of the function given in the graph.

Q: Find an equation for a plane P that: meets the x axis at the point where x = a, meets the y axis at…

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Q: From the table below calculate the quantities asked for: x 84 8 4-6-2-4 f(x) 168 16 8 -12 -4 -8 g(x)…

A: Use the table and simplify

Q: Solve the Bernoulli differential equation: x(dy/dx) + y = y²x²Inx O-1/(xy) = C + x(1 - Inx) O 1/(xy)…

A: First order differential equation :           Consider the differential equation              dydx…

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Q: Find g"(x) for the function g(x) = (x − 3x³)(x² + 1). [A] 6+ 2x [B] 60x4 - 12x [C] -60x³ 12x [D] 0…

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Q: Find (f. f)(x). X 8x + 49 Find the domain of (f. f)(x). (Enter your answer using interval notation.)…

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Q: sinh(2 ln(c))= (A) + 2/2 2c² (B) c² - 1 (C) -2/2/2 2c² (D) c-¹ 1 (E) 0 1:37 AM ✔

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Q: Given the graph of y = f(x) shown below, what is the graph of y = f(x - 4) + 3? -7-6-5 |||||| 3 -I…

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Q: Evaluate the integral: - (6x + 14) (x - 1)(x + 1)² SE dr +C

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Q: Consider the function f defined by f(x) = its domain. a) First compute lim f(x). Answer: XX 5 b a a…

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Q: 6 $ 4 3 = da 2 1 -6 -5 -4 -3 -2 -1 4 -2 -3 -4 The graph above is a transformation of the function…

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Q: 4) Determine the sum for the following geometric series. a) 4+6+9+13.5+...(S₁ b) 280+70+17.5... (S

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Q: Consider r(t) = (2 cos (t), 2 sin (t), −t). Find the unit tangent, unit normal vectors, T (t), Ñ…

A: Given expression: r→(t)=2cos(t), 2sin(t), -t

Q: Find Euler Approximation of the solution y(t) of the IVP y'=2y+3, y(0)=2, within interval [0,3],…

A: Euler's Method yn+1=yn+h.ftn, yn where tn+1=tn+h Given dt=h=1, y(0)=2 or t0=0, y0=2, y'=2y+3 or…

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A: We have to find 1,2,3 and 4.

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Q: 4 9 Find the critical points of the function f(x) = 45x 5 + x 5. Enter your answers in increasing…

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Q: Find the slope of the tangent line to the function’s graph at the given point using the definition…

A: Topic - Limits and equation of tangent line to function we are given,f(x)=xx-2and slope of tangent…

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A: The objective of the question is solving the given differential equations.

Q: 1) Ax B×C 2) AXBXB 3) BX AXC 4) (A-B) x C A = {1,2}, B = {a}, C = {a, ß}

A: Given, A = {1, 2}, B = {α}, C = {α, β}

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Q: 6. 7. 00 8. x = C₁ cos wt + C₂ sin wt; w a parameter y = cx + c² + 1 h y = mx +=;h a parameter, m to…

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Q: Note: Click on graph for larger version in new browser window. The graphs of the function f (given…

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Q: (b) Let f(x) = 1 n<x<n+2, n = 1,2,... 0 otherwise. Prove that f is improperly integrable on (0, ∞)…

A: Please see the below picture for detailed solution.

Q: Suppose that f(x) = 3x² - 4x + 4 and Find the following: 1. (fog) (6) = Number 2. (fog)(0) = Number…

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Q: 4. The movement of a certain glacier can be modelled by d(t) = 0.01t² + 0.5t, where dis the…

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Q: Find ACD, if possible. A = 2-1 0 1 2-3 C = -2 03 3-22 -1 33 D = 1 -2 0-1 3 1

A: Given A= 2-11 02-3,   C= -203 3-22 -133 and D= 1-2 0-1 31To find: ACD

Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: