dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

Q: , X= sin ztS d= In Find dw 2- Cost

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Q: correct to three decimal places by Trapezoidal rule with 1 +x dx Evaluate I= h=0-5.

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Q: se implicit differentiaion to find dy/dx for the curve below. 1. xy3 + 4x2 = tan y2 + 3

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Q: 1) ex-ydx + sin y sec x dy = 0

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Q: can any thing said about the tengent to the curves y=sinmx and y= - sin(x/m) at the origion (ma…

A: Solution  Given

Q: π Q3/ Evaluate Sosyx siny dx dy 0 0

A: Consider the given integral, I=∫0π∫0cosyxsinydxdy perform the integration,…

Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: Differentiate: y = /16 – z² – 4 arccos() e+4 y' = Oy= Oy- %3D

A: Given that : y = √(16 - x2) - 4arccos(x/4). We find derivative of this function (y).       Here i…

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

A:

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

A:

Q: Find the slope of the tangent line to the curve y = x e× at (2.5,2.5 e 2.5). dy (2.5,2.5 e 2.5) dx…

A: We know that slope of a line is defined by , m=dydx. Therefore, we need to take the derivative of…

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: Evaluate the integrals

A: We’ll answer the 15th question since we answer only one question at a time. Please submit a new…

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

A:

Q: O Calculate ........... 2 4-y2 dy dx O I-X ® yde dy

A: Here we will find the solution of question 4. a)∫01∫1-x1-x2dydx Solution: Here the independent…

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: I Approximate "dn with accuracy l by te modified Trapozoidal Compo site rule.

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Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

A:

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Q2/ Delermine area boundled by the curve x'+2x'y²+y%_8x°+8y= 0 t. |

A: Step:-1

Q: Find the derivative dydx of the function x=arctanet, y=1+e2t at t=0.

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Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: 2sin(y)cos(y) sint(y)+costy) dy

A:

Q: Q3: dy\dx off(x)= tan x cot x is

A: Given,    f(x) = tan(x) cot(x)         = 1   As we know, inverse of tan(x) is cot(x).

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

A:

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: Q1-If x= cot- VE, y =, find 2 dy dy dx'dx at t = 2. t+1

A:

Q: 8. Find dy/dx in terms of x and y using implicit differentiaton 5y 4 +x 2 = 9

A: Step for implicit differentiation: (1) Differentiate with respect to x (2) Collect all the…

Q: Show every detail of your solution. Differential equatioens. siny dx + (x - sin? y)dy3D0

A: The given differential equation is: sin y dx+(x-sin2y)dy=0⇒sin y dx=-(x-sin2y)dy⇒dxdy=-(x-sin2y)sin…

Q: what is the equilibrium of dy/dx = y - sqrt(y) when y >0

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Q: Q2 \ Evaluate .1 dx by using trapezoidal rule. 1+x2

A: See the details solution in below

Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: with x=sec t and y=e". Then the value of dz evaluated at dt If z=tan In t= 0 is equal to (Correct to…

A: Given function z=tanln4x2y with x=sect and y=e2t Substitute the x=sect and y=e2t in the given…

Q: Let fx) - V4X-3 vux-3 %3D O Find the arer age rate o ofe change in respect to x aver the intoy vel…

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: I. Find dy/dx in the following: 6. Y=sec² Inx

A: We are given: y=sec-1 lnx The derivative can be found as follows:

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: d. Try to find dx dy at (0, 0) on both graphs. What goes wrong? How does this relate to their…

A:

Q: What is dy/dx of the function y=tanh(sec x)?

A: To find the differentiation of the given function.  y = tanh(Sec(x)).

Q: 9. 2y(у? — х)dy — dx, when x %3D2,у %3D 2

A: Given that: 9.     2y(y2-x)dy=dx,    when x=2, y=2     NOTE: As per our answering guidelines, we can…