Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2 -3 3.

Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: 2. Graph the function f(x) = cos(2x) +1. %3D

A: y=cos2x+1 to graph the function, we need a few points x y=cos2x+1 -2π 2 -7π4 1 -3π2 0…

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: For a given function f(x) the critical point are the value of x at which the derivative of f(X)…

Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x;…

A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

Q: (a) Let f(x) = cos(3x – 2). Find f°"(x). (39)

A: According to bartleby guidelines I can only answer one out of the two questions given.

Q: dx -= In[F(x)]+C. What is F(/3) For (x+x³) (x Tan-lx+ 1) 3. B.

A: We have to choose the correct option according to the given information

Q: | Sketch the midline and the graph of the function f(x) = 1 – 4 cos

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Q: (a) Sketch the graph of f(t) = sin 2(t- π)U(t - π).

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: .Is f (x) = x sinx a periodic function ? %3D

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Q: 57 Sketch a graph of the function f(z) = - 2 sin -1. %3D 4

A: fx = -2 sin x- 5π4-1

Q: b) f (x)=(2x-1ifxsI

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Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin…

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Q: Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin ,…

A: Given  f(x) = sin x4,   0, 8π We have to find the point of inflection and the concavity of the graph…

Q: Q2:- Find the domain of the following functions tanx a) f(x) = %3D sinx-1

A: Domain is value of x for which given function is defined.

Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: Describe with a sketch the end behavior of f(x) = cos x.

A: Given:            f(x) = cos x  The cosine function oscillates between values -1, 1 as x→∞ Hence it…

Q: Find the slope of the graph of the function at the given point.                         f(x) = 5 cos…

A: According to the question, we have to find the slope of function fx=5 cosx-9x at the point 0,5. The…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x + cos…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin x +…

A: The given function is  f(x) = sin x + cos x on  [0, 2 ]. Compute the second derivative as follows.…

Q: Find a function of the form y = Asin(kx) + C or y = A cos(kx) + C whose graph matches this one: 4+ 2…

A: From the given figure, it is observed that the The maximum point on the graph is at -1, that is, y…

Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: 4. How many fixed points does the function T(x) tan(x) have? %3D

A: As per our guidelines, we suppose to answer only one question. Here question 4) is answared.

Q: х — 7 - f(x) = %3D 5х + 7 Find an equation for the tangent line to the graph of f at x = 3.

A: Given: fx=x-75x+7 To find the tangent line, we find the slope Therefore differentiate with respect…

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

A: Obtain the first and second derivative of the given function as follows.

Q: Draw simple graphs of the first and second derivatives of the function y = f(x) whose graph is given…

A: Given,

Q: 16. Use addition of y-coordinates to sketch the graph of the function between x = 0 x = 4 T and 1 x+…

A: Here we have to add graph of y=x/6 and y=sin(x). So the resulting graph will look like as shown…

Q: Sketch the graph of f (x) = 3 cos 2x.

A: Given: y=3cos2x

Q: Suppose f(x) =x²sec( 2x³). Evaluate: dx A -In|sec(2r3) + tan(2x³)|+C sec(2r*) tan( 2r) +C B © sec…

A: topic - indefinite integral

Q: Find the f( for this f (x) = l09, x Cos-lx

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Q: 1 3 1. Find the domain of the function f(x) = + sin V – 6x + 8 2

A: Our guidelines for multiple questions , answer only first question Answer =(1)  We have to find the…

Q: Q3/Discuss the behavior of the following function as x 0: f) = sinx

A: Please rate and feel free to ask any query about any part of the question

Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…

Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: 1 find the domain and range of f(x) 2 - cos3x

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Q: 2:- Find the domain of the following functions c) f(x) = sin¬'(2 – 3x) %3D

A: Solution of the problem as follows

Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: Differentiate the function.

A: Consider the following equation: y=e-2tcos4t Differentiate y with respect to t: dydt=ddte-2tcos4t…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: What is the domain of the function: f(x) = 1/(1 - 2 cos x)?

A: Given,

Q: Express the function in the form f◦g. 2. g(x) =cos2(x).

A: We need to show function as f∘g(x)

Q: Find the local maximum and minimum values of the function g (x) =x + 2 sin x   ,  0<= x <= 2…

A: Given that : The function is g (x) = x + 2 sin x , 0 ≤x≤2π .

Q: Sketch the midline and the graph of the function f(x) = 2 + 4 cos ( x 4 3. 6

A: Given: f(x)=2+4cosx-π4

Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: 4. Consider the function f (x) = 2x + 1. Find the equation of the tangent to dhe %3D graph of f(x)…

A: The given function is                                      f(x)=2x2+1