Determine the value of ſo1 3.1 X cosx dx by using N= 4 of the trapezoidal rule. Round-off to three decimal places. NOTE: LL = 0.1, UL = 3.1.

Q: Given 2(dy/dx)+3y=sin⁡2x,y(0)=6 and using undetermined coefficient method: What is the complementary…

A: We have to find  the complementary solution, yc using undetermined coefficient method.

Q: 1. Use the trapezium rule to estimate the value of the following correct to four decimal places a) |…

A: 1a) It is required to estimate the value of ∫0π3tanxdx with 4 strip using trapezium rule.

Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: a particle travels along the x-axis such that its velocity is given by p(t) = t'. + 3 cos (2t). What…

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Q: 4- Using the data sin(0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin…

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Q: Locate the first positive root of: f(0) = sin(0) + cos(1+ 0²) – 1 Where 0 is in radians. Use four…

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Q: Given (1) Find dy. by applying implicit dx di fferentiation, in (1) (1) explicitly and Solve eg tor…

A: We use the definition of implicit differentiation of a function to solve the given question.

Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

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Q: If the ideal gas law (PV= kT) is used to find P when Tand V are given, but there is an error of 0.3%…

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Q: Determine dy/dx if xy = ecsch(xy)+πcos(0)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. When a pendulum 0.5 m long swings back and forth, its angular displacement O from rest position,…

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Q: The depth of water in Lake Wanaka is given by D(t) = 2 + cos (4t), where D is the depth, measured in…

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Q: So dx 27-x³

A: Given integral is ∫03dx27−x3. We have to solve the given integral. Substitute x=3sin23θ…

Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

Q: The change in heat radiated by a body, detected by a pyrometer (non-contact temperature sensor), is…

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Q: 13. Reduce the equation y + 4 = 0 to the normal form x cos 2 + y sin 1 = p, and hence, find the…

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Q: Solue the Following intial value problem cos?(y)dx + tany dy=0, y(1) = 0

A: Here equation is, xcos2(y)dx+tanydy=0 xcos2(y)dx=-tanydy xdx=(-tany/cos2y) dy

Q: The approximation of I = S cos (x² + 5) dx using simple Simpson's rule is: 0.54869 "-0.93669 This…

A: We have to solve by Using Simpsons 1/3 rule .

Q: Which of the following is equal to J: x2 dx ? A. sin-1 (t) + € B. sin- (t) + € Option 1 O Option 2…

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Q: Find a particular solution Yp = A cos wt and enter the amplitude factor A rounded to 4 decimal…

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Q: Find a possible formula of the form A sin t + k or A cos t + k for the periodic function with a…

A: Given formula is: A sin t + k or A cos t + k

Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: Given x2 + 11x + 30 dx 1 + cos?(x) At what value of t does the local max of f(t) occur? f(t) :

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Q: Consider solving dx using a suitable trigonometric substitution. After performing substitution with…

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Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: Consider the implicit function. e = sin (6x) Determine the formula for in terms of x. dy dx dy dx

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Q: Estimate the values of y(0.2) and y(0.4) for the following DE, using Improved Euler's Method,…

A: we know the modified or improved Euler's method is             y1=y0+12k1+k2 where k1=hfx0,y0 and…

Q: 4 Using n = 8 approximate the value of cos (1+ ya) dx using Using Trapezoid rule, and Display the…

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Q: A particle travels along the r-axis such that its velocity is given by v(t) = t2 cos (3t + 2). What…

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Q: Given the f(x)=cos(x5)+ln(x), find f’(9) at h=0.8 using: (Round off the final answer to 3 decimal…

A: Given that fx=cosx5+lnx Find f'9 when step size is 0.8 using (1) Forward difference method.

Q: Find a particular solution Yp A cos wt and enter the amplitude factor A rounded to 4 decimal places.

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Q: (4) Let the position of a swinging pendulum in simple harmonic motion be given by s(t) = a cost +…

A: Use given conditions to solve for a and b . Please rate and feel free to ask any query about any…

Q: y = 0.78540 + t sin t + 1/8 sin 3t could be used to express the instantaneous value of a waveform.…

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Q: a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

A: To find dy/dx.

Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

A: Simpson's rule error bound    Es≤kb-a5180n4 , where f4(x)≤k where ∣E​S​​∣  this e absolute values of…

Q: A particle travels along the x-axis such that its velocity is given by v(t) = t cos (3t + 2). What…

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Q: Solve the equation below by method of characteristic curve, and check that the solution satisfies…

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Q: e)f[cot2x√sin2x + cos2x]dx

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Q: Find a possible formula of the form A sin t+k or A cos t+k for the periodic function with midline y…

A: The standard equation of any sinusoidal curve is given by  y=Asin(B(t-C))+D      or…

Q: 4) Given y = 3 sin 2x, Find the Amplitude Interval and Period (n2, 0) (0. 0) Amplitude interval =…

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Q: Find the dy + 9 Cos Cx)= 3 Cos Cx) paihular suluhon Of the differenhal epeccin sahisfying the mihal…

A: Topic- Differential Equation

Q: Find the given 5x? cos 2x dx. Using this: "uv – f v du"

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts take

Q: Part 2. Use the integration techniques to solve for the antl-denV 1. 3p? tan p dp Integration by…

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Q: 9. Give an equation for a transformed sine function with an amplitude of 3, a period of I1/4, and a…

A: The standard equation of the sine function: y=A sin (B(t+C)) Where A is the amplitude Period=2πB C…

Q: Consider the implicit function. e' = sin (6x) Determine the formula for in terms of x. dy dx

A: Here we have to find the derivative.

Q: The refractive index n of a piece of glass is related to the critical angle θ by n = 1/sin θ. Assume…

A: The critical angle of a piece of glass is measured to be θ=0.70±0.02 rad. Justification: The form of…

Q: The approximation of I = cos x? dx using composite Simpson's rule with n-3 is: %3D -1.3201 -1.5463…

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Q: 28. Use Newton's Method to find the fourth approximation x4 the solution of the equation cosx =x…

A: we have to find fourth approximation using newton refson method.

Q: (a) Find an approximate value for the integral / cos a dz using the Composite Simpson's rule with N…

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Q: 4. Find an arc distance t, between 0 and 2 (0 ≤ t ≤ 2π) such that sint = sin (117).

A: The given curve is sint=sin11π6 between 0 and 2π