Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , θ lies in quadrant I Find sin θ/2

Q: Given that f(x)=x2+5xf(x)=x2+5x and g(x)=x−9g(x)=x-9, calculate   (a) (f∘g)(5)(f∘g)(5) (b)…

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Q: Population of a certain country is growing exponentially at a rate of 1.5% per year. How long will…

A: Given problem:- Population of a certain country is growing exponentially at a rate of 1.5% per year.…

Q: e² 1+2e +e S Select one: O A. dx 1+6² 2 1+6² +C +C O B. OC. +C OD. +C -2 Ite -1 1+e

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Q: Find the height of the tower using the information given in the illustration. 85.829° 130 A

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y = r sin(8), and note that (x,…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: x = 6 sin 0 is an appropriate trigonometric substitution for the integral Select one: True O False √…

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Q: 1. y (4x + y) dx -2(x²-y)dy = 0 2. (2xy4e + 2xy³ + y)dx + (x²y4ey - x²y²-3x)dy = 0

A: We have to find Solution for given D. E

Q: 8 n = 0 Identify an (-7)" (2n + 1)! Evaluate the following limit. an+ 1 an lim 718 an+ 1 Since lim…

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Q: 10 Find the linearization L(x) of y = e¹0 In(x) at a = 1. (Use symbolic notation and fractions where…

A: Given:   y = e10 ln(x)  At a = 1

Q: -6 -5 -4 -3 -2 -1 5 of f(x) 4 3 2 1 -1 1 -2- -3- N 1 f(x) dx = 0 of f(x) dx > -5 Which of the…

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Q: (a) √ (cos r - sin r) da (b) / cot² x da

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Q: To evaluate the integral I cos cos4 x sin3 xdx we save one sine factor and use sin² x = 1 cos²x to…

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

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

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Q: the region enclosed by y = e¹¹, y = 5², and a e = 1. Find the area of the region.

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Q: Find the area of the triangle with vertices P(1,3, —5), Q(0, 0, 0) and R(4, 5, 1). NOTE: Enter the…

A: The triangle with vertices P1,3,-5, Q0,0,0 and R4,5,1

Q: Decide if Rolle's Theorem can be applied to f(x)=x² - 4x² + 4x² +1 on the interval [-1, 3]. If…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

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Q: Integrate | VE 1-4x² dx using a trigonometric substitution.

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Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

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Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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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: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

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Q: Sy²sin (2y) dy

A: Integration by parts.

Q: 3) Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is…

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Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: The integral is improper. Select one: True O False 2 [₁² 2x -3 x² - 9 - dx

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: Find the unit tangent vector to the curve given below at the specified point. r(t) = 7ti−2t²j¸ t = 4…

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Q: Integrate √1 - r²dr Select one: OA. }(arcsinx+v1_2)+C OB. }(arcsinx+2v1_z)+C OC. (arcsinx +…

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Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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Q: 1 SSR (x+y)² dxdy

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Q: x³ 3x²+5 (x-3) S - x³ - 5 In 1 x-31 + C Option 1 dx x³+5 In Ix-31+ C Option 3 x3 3 Option 2 x3 - 5…

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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: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

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Q: Find the derivative. h(x)=2x^3−5x^2 / x+2 You must show

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Q: Divide using synthetic division. (x 2 + 15x + 54) ÷ (x + 7)

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Q: Choose the correct answer for the following limit: lim (x,y) →(0,0) O -1 0 1 625 x¹-16 y 100 x² +16…

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Q: The graph of the first derivative f' of a function f is continuous on (-∞0,00). -2 -1 2 3 (e) Find…

A: The graph of the first derivative f' of a function f is continuous on -∞, ∞. e To find the…

Q: Work problem 2 ( } Let w(u, v) = 5u - 5v + u³ - 5v³, u = cos(21) and v = u —sin(3s). Use chain rule…

A: In this question, we will use chain rule to find all the derivatives of w.

Q: The value of the integral is: b 12 f(x) dx = a

A: Given that the graph of the function  To find the definite integral that represents the shaded area

Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: The gradient vector of the function f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-1,-2). Select…

A: This question is based on gradient of function at a point.

Q: Find the area of the triangle with vertices P(1, 3, −5), Q(0,0,0) and R(4, 5, 1). NOTE: Enter the…

A: The objective of the question is determine the area of the given triangle .

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: Is it possible to have it a little more detailed?

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Q: 6 (2) Find and draw the Fourier transform of f(t) = 9+t²

A: Find and draw the Fourier transform of f(t)= 6/(9+t^2)

Q: f(x) = X X+1' a = 1; f(1.2)

A: topic - linearization of a function

Q: √(√3+)dx Select one: OA. OB. OC. OD. ³/2-² + 4x¹/2 + G ³/2² + 4x¹/2 + G ³/2² + 4x¹/2 - ³/2x² + с +…

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