Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , tan θ > 0 Find cos θ/2

Q: Let f(x) = X x - 3 g(f(x)) = and g(x) = 4 X Find the following functions. Simplify your answers.…

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Q: ex-4e-x ex 2 x-² / + C ex Option 1 dx 2 x + ² + C ex O Option 3 x+2 ex + C O Option 2 x-2e * +C O…

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Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: Sketch the function y = 7x on the interval [0,5] and let R be the region bounded by y = 7x and the…

A: In this question we have to sketch the function as per the given statement.

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: An aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

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Q: Find the first partial (a) derivatives of the function f(x, y) = x²y√√√y + 4y². (b) fxyx of the…

A: A two variables function f(x,y) is provided. We have to find the first partial derivatives and…

Q: Let F(x) = = (x − 3)³ − 4 cos (x-3) Find lim F(x). x 3 + lim F(x) = x+3+ x < 3 3 ≤ x

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Q: 16. Write an equation for the transformation of f(x) = |x| shown in the graph below. V

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Q: directional

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Q: x(t) = £−1 x(t) = L−¹ S s² +5 3s² +9 4s ((s + 3) (s+5))

A: Last 2 question solved

Q: Solve Problem 346 in section 4.7 of the textbook. In addition to providing the calculations, draw a…

A: Solution is given below:

Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: A rate of change of H is given by Solve for k where H > -25. O 0.458 O 0.346 0.255 O 0.144 dH = k…

A: topic- differential equation

Q: The number of oil changes per hour at Quick Lube is described by the following short-term production…

A: answer is in next step .

Q: A tank is is half full of oil that has a density of 900 kg/m³. Find the work W required to pump the…

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Q: Integrate farcsin 3x da Select one: O A. xarcsin 3x + √1-9x² + C O B. xarcsin 3x + √1-92² +C O C.…

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Q: (b) r4 x x²-9 dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Integrate 3+22 Select one: OA. 7Inlxl + OB. 4inlxl + O C. 31nlxl + O D. 5Inlxl + dz + C + C + C + C

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Q: Use the given information to find the exact value of the trigonometric function.  cos θ = 1/4 , csc…

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Q: 8. Solve the differential equation: y' √x 7y

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Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: To find the minimum distance from a point to a paraboloid is just to minimize the function…

Q: Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the…

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Q: Work problem 1 Consider the ellipsoid given by the equation: .8 53 - 5z². X + y 4 8 a) i ]Find the…

A: Let's find equation of tangent plane and normal line.

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given problem:-

Q: Integrate fx cos(4x) dx fa

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Q: 60° a 100° 5 b A

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Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

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Q: Integrate Ja giả Select one: OA. 2-x dz Ina-Inx+5| + C OB.Inx-lnx +51 +C OC. In x-lnx + 5+ C OD.…

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Q: The rate of change of N is proportional to 20 + N(x), where N < −25. If N (0) = 10, and N(2) = 25,…

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Q: The rate of change of N is inversely proportional to CSC(x) · N(x), where If N () = 1, and N (5) =…

A: Given: dNdx∝1cscx.N

Q: The rate of change of N is inversely proportional to N². IfN (0) = 4, and N(2) = 6, what is N(5)? O…

A: The rate of change of N is inversely proportional to N2N(0)=4 and N(2)=6

Q: Consider the following. w = x - ¹₁ x = e³t, y = t³ (a) Find dw/dt by using the appropriate Chain…

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Q: Evaluate the given integral: 2 fлсoе² (2x) dx

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Q: (a) [2 2 2x dx

A: Note: As all are different questions, as per our company guidelines we are supposed the answer the…

Q: Find the critical value 5x+1/x

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Q: D O 1.909 Question 14 Find the length of the plane curve given below. r(t) = 5cos(t)i+5 sin(t)j, [0,…

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: Use the function to show that f(0, 0) and f(0, 0) both exist, but that f is not differentiable at…

A: Concept: Partial derivative: In differential geometry and vector calculus, the partial derivative is…

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y),…

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Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: Differentiate and simplify this function:  e√t^2+t+1 - e-√t^2+t+1

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Q: Determine the area of ​​the region bounded by the curves y = x3  , x + y = 2 and y = 0

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Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

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Q: Find the derivative of the following function. g(x)= 1+cos x / x + sin x

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Q: Consider the following function. f(x) = (x - 3)ex (a) Find the critical numbers of f. (Enter your…

A: We have to find the critical points, monotone intervals and relative extremum.

Q: Use the implicit differentiation to find dy/dx. Then find the slope of the curve at the given point.…

A: By using the implicit differentiation to find dydx. Then to find the slope of the curve at the given…

Q: Determine the continuity of the function f(x, y, z)= O continuous except at (0,5, 0) O continuous…

A: topic- continuity of a function

Q: Evaluate the integral S dx 25+225x²

A: Given, ∫125+225x2dx