(1) What are the six basic hyperbolic functions? Comment on their domains, ranges, and graphs. What are some of the identities relating them?

Q: Differentiate the following hyperbolic functions

A: Consider the given hyperbolic function y=log5sinh e9x2.

Q: What is the fundamental identity for hyperbolic functions?

A: Hyperbolic functions have identities that are similar to the identities for trigonometric functions…

Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: Given: The function y=cos3x and the point π4, -22, To determine: The equation of the tangent to the…

Q: Below is the graph of a trigonometric function. It Intersects its midline at and it has a maximum…

A: I have provided a solution in step2.

Q: Based on the theorems, obtain the fixed points of the following function.

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Q: Sketch the graph of f(x) = 2x + Vx*.

A: Given that we need to Sketch the grah of  y = 2x1/3 + x4/3  Now,  The graph is as follows

Q: The top of a bucket 0.5 meter high is attached to a water wheel of diameter 5.5 meters. The wheel…

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Q: 12 of 17 > Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point…

A: We have to find equation of tangent plane for the given Curve.

Q: Sketch the graph of the function. Show complete solution on the upper half of the graphing paper…

A: Given funciton: fx=sinx+π3 Now we know that, sine curve can be written in the standard form,…

Q: 1. Verify Rolle's theorem for the function (x+2)' (x-3)* in the interval [-2,3]. Plot the curve…

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Q: Find a formula for the trigonometric function shown in the graph. 0.7 -0.7 y(0)

A: As we can clearly see the above graph is periodic in nature and is very similar to sin function…

Q: Sketch a graph of the function f(x) = 4 cos|

A: Steps to draw the graph 1.) Plot cosx

Q: a.) What is the Standard Form and General Form of the Parabolic Function? b.) What is the Standard…

A: The solution is follows: b)for the semi ellipse , f(x)=baa2-x2  where a  is the horizontal half-axis…

Q: Below is a value of cosh x. Use the definitions for hyperbolic functions and the identity coshx-…

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Q: Question 4 Does the graph of g(a) = x? x sin(1/a), "completed" by defining g(0) = 0, have a tangent…

A: Given that g(x)= x2sin (1x), x≠00, x=0

Q: This exercise explores the effect of the inner function g on a composite function y = f(g(x)). Graph…

A: Let us draw the graph of both the functions:

Q: 8. For the function y = -2 sin(r), complete the following table using the standard "5 points"…

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Q: 6. Describe in words the transformations that must be applied to the graph of f(x) = sin x to obtain…

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Q: True or False The graphs of y=sin x and y=cos x are identical except for a horizontal shift.

A: Given- y=sinx and  y=cosx. To Check- If The graphs of the above expression are identical except for…

Q: Match the trigonometric function with one of the graphs -VI. Graph 1, 2, 3, 4, 5, or 6 f(x) =…

A: Match the trigonometric function with one of the graphs I-VI  f(x) = sec(2x)

Q: 14. Sketch the graph of the trigonometric function in 2 periods. You have to show the intercepts and…

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Q: The derivative of the trigonometric function y = x csc 3x is A. -csc 3x ( 1 + 3 cot 3x) B. csc 3x (1…

A: d(u.v)dx=u.dvdx+dudx.v  [ Product Rule of differentiation ] d(csc (x))dx =-cot(x)csc(x) dxndx=nxn-1

Q: Use the asymptotic behaviour of f = sin(πx) + xe^−x to sketch its graph. Include the graphs of y =…

A: Use the asymptotic behavior of f=sinπx+xe-x to sketch its graph. Include the graphs of y=xe-x and…

Q: 1. Consider the graph of the sinusoidal function given below. 3- (105, 2) 2 1- -150 -75 75 150 225…

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Q: Match the trigonometric function with one of the graphs l-VI. f(x) = sec(2x) Graph 1, 2, 3, 4, 5, 6…

A: We will use the trigonometric graph to find solution to the problem .

Q: Given the cosecant functions of y = csc-), find the equation of all of its vertical %3D asymptotes.

A: y=cscx2-π2⇒y=1sinx2-π2     ∵cscx=1sinx

Q: For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable.…

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Q: Graph the function by hand, not by plotting points, butby starting with the graph of one of the…

A: For plotting the function, first plot the graph of the function y=sinx.

Q: The tangent to the graph of f(x) = 1/x^2 at point (2, 1/4) form a triangle. Find the area of the…

A: Given query is to find the area of the triangle formed by tangent.

Q: 3. Plot one cycle of the function below on the grid provided. (5 marks-A) f(x) = 3 sin ( 2x + - 1 2…

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Q: Identify the graph of the curve by first sketching the graph of r as a function of 0 in Cartesian…

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Q: 1 Find the Domain and Range for y = 1-√5-x Graph and find the domain and range for y = sin²x + 1

A: 1) The given function is: y=11-5-x

Q: Find the exact value of the function: arcsin(1)

A: arcsin1 can be written as sin-11. The value of sinθ is equal to 1 when θ=π2.

Q: A rope of length 8 feet is arranged in the shape of a sector of a circle with central angle 0…

A: Rope with 8 feet length is arranged as shape of sector of a circle.

Q: f faiy) =V x y+1.SinXy

A: Given :-  The Given function is :-  f  x , y  =  x2 + y2 + 1 . sin xy To Determine :-  fx , fy , fxx…

Q: Sketch the graph of the function. y = 3 sin 2x/5

A: We draw a table with different values of x and y. x y 0 0 1 1.168 -1 -1.168 2 2.152 -2…

Q: 2. The graph of the function y = Sin x is transformed by vertically compressing it by a factor of 1…

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Q: How do you solve this and can you show me step by step?

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Q: Sketch the graph of the function. Show complete solution on the upper half of the graphing paper…

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Q: (5) Here is a tangent function: g(x) = tan (3x -) Please answer each of the following and consider…

A: Horizontal shift : π/9 Solution :- 3x-π/3 =0                     x= π/9 Right side horizontal shift…

Q: Find the algebra expression of Hyperbolic functions: a). sin and cosine b). cosine and tangent

A: Hyperbolic functions are analogues of the ordinary trigonometric functions, where it is defined…

Q: Sketch the graph of the function. Show complete solution on the upper half of the graphing paper…

A: f (x) = 2 cos (x-2π)        =2 cos (x)                              ∵period of cos(x) is 2π

Q: į Which of the following is the best description of the contour graph Question 12.- for the function…

A: Contour graph: A contour graph is the technique to represent a three dimensional surface of the…

Q: Consider the ecuation. Where a,b,c ,d are given regular functions.   If the equation is…

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Q: sketch their graphs y = 2 sin (x + π) - 1

A: Here we have to draw the graph of y=2sin(x+π)-1 since it a sinusoidal curve.....

Q: 8. Explain how to graph the of y = csc(x) with respect to the graph of y = sin(x) and sketch both.…

A: For drawing csc graph 1st we will draw graph of sinx.

Q: Sketch two complete cycles of the following trigonometric function. Include mapping notation of…

A: Given equation of the curve is: y=-3cosx-45+2

Q: Graph the function by hand, not by plotting points, butby starting with the graph of one of the…

A: Definition used -          For trigonometric function -                       y =sinx…

Q: Can you please solve these two sub questions and show the work

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…