Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: Where does the graph of the function y=3•cos¬lx-sin¬'x have a horizontal tangent line? Provide an…

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Q: Find cosh 2x sinh? 2x dx.

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Q: Show that y = tanh x is an odd function.

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Q: d cosx)= -sinx dy lim Cos(Xth)-coslx) ha0

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Q: Show that y = tanhx is an odd function.

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Q: FInd the intervals in which the function f(x) =sin(logex) +cos(logex) is decreasing

A: Given function is, f(x)=sin(logex)+cos(logex)

Q: Evaluate: [ cos 2x log(1+ tan x) dx

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Q: Compute the derivative cos(sin(e7))

A: cos(sin(e7)) We need to find the derivative of the given function.

Q: Solve the equation for x. arccos x = arcsec x

A: Concept: Calculus involves the study of rate of change, which is used to calculate the objects which…

Q: Find the derivative of the following function: 5. sin (cos(x))

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Q: 1. y = sin(4x) 2. y = sin(4(x - )

A: We need to find period of given function.

Q: In the given question, verify the identity:- sinh(x + y) = sinh x cosh y + cosh x sinh y

A: Consider the provided identity, sinhx+y=sinhx coshy+coshx sinhy Verify the provided identity.…

Q: , I- Se* . sinh 2x dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Find y' if cosh x sinh?

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Q: In the given question, verify the identity:- cosh x - sinh x =- e-x

A: As we know that the hyperbolic function of the inverse trigonometric identity is given by as…

Q: Using appropriate substitution, f sin°(x)cos³ (x)dx is equal to:

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Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: ind the derivative of the function y = (x+ 8 sinx) (1+ 14x), and simplify the answe

A: Given : y =(x+8sin-1x ) ( 1+14x)

Q: What is the derivative of sin? x f(x) = with respect to x? COs x

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Q: sinh(In In a)da is equal to xlnx

A: To find:∫sinhlnlnxxlnx dx

Q: Find using IMPLICIT DIFFERENTIATION by following the steps below. y = arccos(5r + 1), or in other…

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Q: Find the trigonometric integral ∫x tan4 x2 dx

A: Given: I=∫xtan4x2dx for evaluating given integral, we substitute  x2=t…

Q: y = e*In(sinh x)

A: See the details solution in below

Q: +(x)=sin' (tan 3x) 1-

A: Since you have posted multiple questions, as per our policy we will answer first question. please…

Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

Q: How many periods of the function y = tan x are there between -27T and T? %3D [?]

A: We have to find

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: /x[cosh?(2x²) – sinh²(2x²) ]dx is equal to

A: solution :let…

Q: The equation Te" +3e can be expressed usin g sinh(x) and cosh(x) as:

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Q: Differentiate the following functions: 5. y = sin-(n(2x + 1))

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Q: At what points are the functions continuous? = |x - 1 | + sin x

A: y=|x-1| is continuous for all values of x y=sinx is also a continuous function.

Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: Express the following as an algebraic function of x. sin(arctan(2x) + arccos(2x))

A: Question is solved.

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: Find y' and y" by implicit differentiation. cos(y) + sin(x) = 1

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Q: a (a) L{sin at}=- s2 +a?

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Q: Write the definitions of the hyperbolic functions , sinh  x  ,cosh x , tanhx

A: Solution:- Definition of the hyperbolic functions, a) sinh x b) cosh x c) tanh x

Q: 1) Compute each derivative, show all work. Submit your work as a pdf. a) sin (1+ e3a b) tan (3x? +…

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Q: Express the following as an algebraic function of x. sin(arctan(2x) – arccos(2x))

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Q: Find the arc length of f(x) = In(sin(x)) for - 10 8

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Q: If f(x) = 3 sin(4æ) arcsin(x), find f' (x).

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Q: As x gets closer to zero, tan2x/ln(1+x) gets closer to what value?

A: This question can be solved using the concept of L HOSPITAL,'S RULE.

Q: find the implicit formula of sinxy=x+y

A: Given,

Q: y = [cosh(ln x) + sinh(ln x)] 2

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Q: Solve without a calculator: lim (sin (7h) / h) as h approaches 0.

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Q: What is the derivative sin?x+cos?x

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Q: please differentiate the function provided in the images

A: Given that