ĮY = cos (y)x³ y(0) = 5 Solve the IVP , and then evaluate lim y(x). Return only the latter x--00 as your answer. 4.7124

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A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

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A:

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A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

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A: Consider the limit

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A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

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A: This is 0/0 form so use L hospital rule and Solve.

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A:

Q: 11. Use definite integrals to show that f(x) = x² – 3 and g(x) = 5 – x² have the same arc length on…

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A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

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A: Given, cosh(x)=5, x>0

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Q: 1 8. When we say that (Inx) = , we really mean to con- dx 1 on the restricted domain (0, 0). sider…

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A: These questions are related to limits, we will solve them using given information.

Q: 2x? — х — 1 lim b) х--1 4 — 3x? — х x² + 3x +1 lim x→-1 2x? – 3x – 5 а) VE- 2 m³ – 8m + 1 lim lim -…

A: e)

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Q: 1) 土七 COS ant5 Sinant3 an: 2then fird the m lim 3) D. Ehmit does not exist

A: Given query is to find the limit of the expression.

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Q: Consider the following initial-value problem y' = (y-1)°cos(Ty), y(0) = 1.29 %3D Without solving the…

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Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: - While working with a colleague you encounter the following initial value problem: dy (2² – 9) -…

A: From the Peano's theorem,

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Q: 1. Calculate for one real root of tan x = 4x with xo 1.2 %3D up to six decimal places using the…

A: Ques : tanx=4x f(x) = tan(x)-4x f'(x) = sec2(x)-4 x0 = 1.2 By Newton Raphson method xn+1…

Q: Q3/ Solve the following. 1. lim(1 + sin4x)cotx X-0 Inx 2. lim X→∞ √X

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A: The concentration C(t) is given by C(t)=sint+cost-1   , on the interval 0,π2             .....(1)…

Q: 42. 1 B. arccosh x x Va² + x² 1 43. С. | —arccoth x x Va² – x² 1 - 44. D. -arccsch x Va2 + x2 45. 1…

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Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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Q: 7. A particle travels on the x-axis so its velocity at time t is given by v(t) = ÷- sin t, for 0 <t…

A: In the question it is asked to calculate value of time t for which the particle moves to the right.

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Q: e Lim 2. 5+s2 y4 3 Lim (4) Lipn J+ Cos늦

A: 1. lims→∞(ss+1)(s25+s2)lims→∞s×s2s×s211+1s11+5s2= 12×2=14

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Q: Q4. Find the root of the equation Cos x-x = 0 near to 0.5 using Newton-Raphson method correct up to…

A: Let  f(x) = cos x - x2 So,  f'(x) = -sin x - 2x Given x0 = 0.5   Newton-Raphson formula : xn+1 = xn…

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Q: cos (T + h) + 1 41. lim h 0 1o dyhori of onil

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Q: 23// Use Newton-Raphson Method to solve f = -x²+x+0.75 for 5 iteration (choose 4-decimal places).…

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