Evaluate exactly lim (1 + sinx)²cotx x→0

Q: Q5) Evaluate the following integral by using Partial Fractions Method = y = S₁ 2x²-3x+2 - (x − 1)².…

A: Use partial fraction to calculate the integral.

Q: Solve 2 cos² (t) - 3 cos(t) + 1 = 0 for all solutions 0 ≤ t < 2π t = Give the exact answers as a…

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Q: 1. Using the diagram below, fill in the blanks. B A D G F H E Column A: a) AB+ BC b) FE+FG c) HG+FB…

A: We need to fill in the answers.

Q: 22. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: “Since you have posted multiple questions, we will solve the first question for you. To get the…

Q: ²²1559 1≤ y ≤9 Find the length of the curve_x==y 3

A: If if x is a function of y then  the length of the curve is L=∫ab1+dxdy2dy   over the inetrval a≤y≤b…

Q: In the figure, the equation of the solid parabola is y=x²-4 and the equation of the dashed line is y…

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Q: For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length of…

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Q: 5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001…

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Q: Consider the following. f(x) = =x+4 (a) State the domain of the function. O all real numbers x O all…

A: We have to find asymptote

Q: Sketch the graph indicating maxima, minima, asy 4-x³ function: f(x) = x3

A: Given: f(x)=4-x3x3

Q: As a result of losing a tug-of-war match, Mr. T is in the middle of a ditch. A group of people…

A: This question can be solved using the concept of vectors.

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: topic- average value of function over interval

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: Recall:., To find Average,  Ave=1b-a∫abS(t)dt We have, S(t)=600 et, a=1, b=5

Q: x dx + (y - 2x)dy = 0

A: To solve a homogeneous differential equation of the form dydx=f(x, y), it is easy by making the…

Q: Find the derivative of the function. 11 y=x¹¹ ex y'=0 V

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Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: First we find the limits of integration.

Q: 8 Y + 2√² + 2y = 10x + 25

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Q: Find the cumulative density function for the given probability density function. k(x) = 0.8 -0.8x,…

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Q: deltamath.com/app/student/solve/16352325/custom1653336005825 Slide Carnival Home | Schoology Click…

A: To find the augmented matrix.

Q: Graph the rational function. -5x-15 f(x)=- x²+2x-15

A: Graph the rational function :      f(x)=-5x-15x2+2x-15 Start by drawing vertical and horizontal…

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

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Q: Find the mass of a wire in the shape of helix_r(t)= cos ëti+sinät j+8tk, 0≤t≤1, where the density of…

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Q: Find the area of the region between f(x) = x² + 2 and g(x)= x - 1 on the interval [-2,2]

A: The functions are f(x)=x2+2  &amp;  g(x)=x-1

Q: 1. a) Given the lines L₁ : 7 = (1,2,−4) + t(k+ 1,3k + 1, k − 3) and L₂: x=2-3s, y = 1-10s, z = 3-5s,…

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Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

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Q: /sin-¹ (√x) dx tegral.

A: Let I=∫sin-1x  dx

Q: 2x + y + z = 1. 7. Find the tangent vector r' (t) and unit tangent vector T(t) at the point with t =…

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Q: 4. A plane travels on a bearing of 15° at an air speed of 655 km/h. It encounters a wind blowing at…

A: Given the air speed of the plane is 655 km/h at a bearing of 15°.  The wind speed is 45 km/h at a…

Q: e)f[cot2x√sin2x + cos2x]dx

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)k+1k!…

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Q: Use the root test to determine whether the series converges or diverges. If the test is…

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Q: Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated…

A: We use the property of the log function to determine the value of x

Q: Explain why the integral is improper. 49 1 1²0 √/x dx 1.6 1.4 1.2 Y 08 0.6 0.4 0.2 10 20 X At least…

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Q: is: The value of the following limit Lim (cos(x))ou(x)

A: The value of the limit is when x tends to 0 for the function (cos(x))cotx

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

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Q: Use the Lagrangian method to minimize f(x, y, z) = x² + 2y² + z² s.t. x² + 2y + 3z = 8 Find the…

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Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

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Q: Determine whether the function defined is one-to-one. f(x)=√/32-x² -X www Is the function…

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

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x₁ = 2 be the…

A: answer is in next step

Q: 27. Check whether the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a ight angled…

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Q: Using the Law of Sines to solve the triangle if ZA = 41°, ZC = 73°, b = 22 LB is degrees a = C =…

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Q: Find the derivatives of the following functions as specified: f(x) = sin(cos r), f"(x)

A: Given: so,       f'(x)=sincosx'         =coscosxcosx'          =coscosx-sinx         =-coscosxsinx

Q: A horizontal trough is 1600 cm long and its ends are isosceles trapezoids with an altitude of 4 m, a…

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

Q: For the matrix B shown below, determine the value of the element b32. If the element is not defined,…

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Q: hand written plz 6. Find the general solution of the PDE. The solution u is a function of x and y.…

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Q: Determine the area of the region bounded by the curves y = x4 - x2 and y = x2 - 1

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Q: d the mass of a wire in the shape of helix r(t) = cos лti+sin лtj+8tk, ≤t≤1, where the density of…

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Q: x2 dx+(x3+y6+2y5)dy Give an implicit solution

A: we need to find out the solution of the differential equation.

Q: Question Use the graph of f(x) shown below to determine each of the following limits. If any of the…

A: Given graph of a function f(x).