Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by F (t) = 82 + 4 sin (÷) where F(t) is measured in cars per minute and t is measured in minutes. To the nearest whole number, how many cars pass through the intersection over the 30-minute period? cars

Q: differentiate the given function 4. f(w)= sin(w)+ w* tan' (w) solve it on paper

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Q: Where are the functions f1(x) = ∣sin x∣ and f2(x) = sin ∣x∣ differentiable?

A: We graph f1(x) = ∣sin x∣  using a graphing calculator. We see that, at x=nπ, there are cusps.…

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 1/4 3/8

A: We have given  ∫x sinx cosx =fx sin2x-gx cos2x+C Let,  I=∫x sinx cosx dx I=∫x sin2x2dx I=12∫x sin2x…

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1/4

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Q: 6. Use the Successive Approximation method to find correct to four significant figures a real root…

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Q: What is the range of the function f(æ) = 23 sin 4w+1 ?

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Q: Find the local maxima and minima of the function sin(x) f(x) 3+4 sin (x) 2 on the interval [0, 27].

A: Given,           f(x) = sin(x)3 + 4sin2(x)  and interval =0, 2π

Q: 1 Find f"(x) for the function f(x) %3D (2+sin x)=

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Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

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Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

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Q: (В) f (x) 3 3 sin(2x) — 4

A: we have to draw the curve of the function fx=3sin2x-4 let y=f(x). therefore, y=fxy=3sin2x-4 the…

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Q: Consider a function f(x) where f" (x) = 2ª (ln 2)² + sin(-. -). 2 a) Find / f"(x) dæ. b) Assume that…

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Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: Given the function f(x,v) = *ye6-sin²x e cos?x The second derivative f, of f is equal to 0. Select…

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Q: Determine the lowest positive real root of f(x) = 8 (Sin x) (e-*)–1 using the Secant method. Take…

A: Solution: Given that

Q: Find the absolute extreme values of the function on the interval

A: Refer to the question we have to find the absolute extreme values of the function provided on the…

Q: Consider the function f(x) whose second derivative is f''(x) = 9x +8 sin(x). If f(0) = 4 and f'(0) =…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinax dx=-cosaxa+c ∫cosax dx=sinaxa+c ; where 'c' is an integration…

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Q: Apply the method of Example 6 to f (x) = sin x to determine f ' ( π/4 ) accurately to four decimal…

A: Given function is fx=sinx. To determine f'π4. Solution: Function is fx=sinx. Differentiating the…

Q: The height of an arch above the ground is given by y = 10 sin sin x , for 0 < x < T. What is the…

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Q: For the function f(x) = sin x , with the aid of elementary formula sin2A = 1/2 (1 − cos 2A), show…

A: Given that fx=sinxfx+y=sinx+yfx+y=sinx cosy+cosx siny by addition formulaNow ,       fx+y-fx…

Q: The derivative of y = 3 cos (V1-x²) + (1-x²), can be written as sin ( V1-x² ) – ( 1–x²) }) 3x…

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Q: Consider ! x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

A:

Q: Find a function F(x) satisfying F'(x) = sin(6x).

A: Solution  Let consider differential  F'(x)  of function F(x)  so F(x)=∫F'(x)…

Q: If f(x) = => (1- (sinx)?)" .Determine the value of f( %3D n=1

A: by using geometric progression

Q: Consider the function f(x) whose second derivative is f"(x) = 7x + 10 sin(x). If f(0) f(x)? 3 and…

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Q: Č) ´It is given that f(x) = tan¯"(1 +x). (i) Find f(0) and f '(0), and show that f "(0) =

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Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Accurate to 5 decimal places and in 0% approximate error, find the root of f(x) = sin x - 1/3 x, in…

A: The given function is fx=sinx-13x in the interval 2,2.5. Calculate the Accurate to 5 decimal places…

Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an…

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Q: Consider the function f(x) whose second derivative is f"(x) = 10x + 10 sin(x). If f(0) = 4 and f'(0)…

A: Given that: f''(x)=10x+10sinx

Q: Find (f −1)'(a). f(x) = 4x3 + 5 sin x + 2 cos x,    a = 2   (f −1)'(a) =

A: Consider the function f(x) =4x3+5sinx+2cosx.Compute the derivative of the given function as follows

Q: Зп /2 | sin(x + 7)| dx

A: To evaluate the integral ∫03π2 sinx + π dx

Q: What is the relationship between the domain of a the function y = sin x and the range of the…

A: Topic:- range and domain of trigonometry function

Q: 4 If f(x) = sin* a, find f'(x). %3D Find f'(2).

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Q: Given the functions f(x) = 1-r and g(x) = cos x determine an equation for h(x) = Ag(x)) and write as…

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Q: Find the x-coordinates of the points of inflection of k(@) = sin (e) on the interval 2 Use exact…

A: h(θ) = sin2(θ)  [ -π/2, π ]

Q: If f (x) = - sin(x), then f (11) (x) is equal to A - sin(x) B - cos(x) sin(x) D cos(x)

A: Differentiate 11 times

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(7) = 2.

A: Given: f'(x)=sin(x)+cos(x)+1 and f(π)=2

Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

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Q: f (x) = cos(3æ) – sin(x), xo = 0

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0)…

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Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

Q: Find the linear approximation of f(x)=sin(x) at x=2π3 and use it to approximate sin(121∘). Give…

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Q: iate the following functions. Show the complete solution. 1. ?=tan?+3csc? 2. ?=sin?+sec?−4ln? 3.…

A: Differentiation: y=tanx+3cscxdydx=sec2x-3cscx .cotxy=sinx+secx-4ln xdydx=cos x-secx tanx-4x

Q: 1. (a). Find the linear approximation to f(x) = sin x at = 0, (b). use it to approximate sin(-0.01).…

A: We have to find the linear approximation and percentage error.

Q: 4) Differentiate the function, and simplify the result. w(x) = sin /2r + 1

A: w(x) = sin √(2x+1)

Q: On which interval is the function f(x) = 3 sin(2x), 0 <x<7, decreasing? O 0 < x < Зл 4 < x < T * < x…

A:

Q: Find the function f(x) if f'(x) = 2 cos x + 3 sin x and f(0) = 4

A: We have