= tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: EX / Show that cosh x-sinhx=1

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Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = θ + sin2 (θ/3) - 8, (-∞,…

A:

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

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Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: By using the definition of hyperbolic functions, show that sinh x = 1 (cosh 2x – 1). -

A: Given,         sinh2x=12cosh2x-1

Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: the length of the curve y = coshx 1sx<2 is sinh(2) – sinh(1) Select one: O True O False

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: lim 3 2y ソ→o ソーSiny -sin.

A:

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: Justify the hyperbolic function based on the six hyperbolic functions: 1. sinhx coshx

A: To Examine: whether sinhx=coshx or not, using the definition of the hyperbolic function.

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: Find an equation of the tangent line to y=10sin(x) at x=π / 6 (Use symbolic notation and fractions…

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: */16 etan(1r) sec2(4x) dr

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Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: Use Secant method to find the root ofthe function:f(x) = 3x + sin x- e to 5 decimal places. Work…

A:

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy %3D

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Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: 8. The value of f sinh* x cosh³ x dx

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Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: If sinh(x) = 35 =, find the values of the other hyperbolic functions at x. %3D cosh(x) tanh(x)…

A:

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Use the Intermediate Theorem show that there is a root of the given equation: sin a - x between…

A: Intermediate value Theorem states that if f is continuous on the interval (a ,b ) and L is a number…

Q: I* cos z lim 1³+2

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Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: Find the equation of the tangent line to f(x) 16e* cos2(x) at x 4 (Use symbolic notation and…

A: To determine the equation of the tangent line.

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

A:

Q: limit x approaches zero, sin^2x/x

A: Given,