(b) Prove that : - 1) (coshx)² – (sinhx)² = 1

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: Estimate the root of 2 cosh x sin x 1, using the secant method, with an accuracy of 4dp. Take 0.4…

A: Image is attached with detailed solution.

Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

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

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Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: 2. Evaluate the integral: | sinh x cosh² x dx

A:

Q: If y- sinhx then prove that = dx

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

Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

A:

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

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

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Q: sin(2t)dt 0,

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

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

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Q: Use linear approximations to estimate the following. 1. sin 9/4

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Show that (i) | te 3 sint dt 50 -3t %3D

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

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: Find a real root for x tan x+1 = 0 using Newton Raphson method.

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Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

Q: at æ = 0 for 12 sin(t)dt.

A:

Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

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Q: Use the Newton-Raphson Method to approximate the root of f(x) = 2 cos(x) – 2x + 1.

A: Newton Raphson method: numarical methods

Q: Find an approximate solution, accurate to 5 decimal places, to the equation cosx=x2 that lies in the…

A:

Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

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: Find fif f'(0) = 2 sin 0-sec²0

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Q: I* cos z lim 1³+2

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Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

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: Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…