Vsinte-sinh²t, dt using 12. Find the leading asymptotic behavior as x tends to infinity of Laplace's method.

Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = ex sin y at the origin. Estimate…

A: The given function is,

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: - 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 root of the equation  f(x)= -x/2 + sinx =0 using bisection method in the interval [1,3]…

A: given function fx=-x2+sinx=0 find the root of the equation using bisection method in the interval…

Q: For the slope field shown, which could be a family of anti-derivatives?

A: To determine which of the equation is a family of antiderivatives for the given slope field.

Q: Integrate the following function by using trapezoidal rule. 142*dx

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Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

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Q: Q3 Use Secant Method to find the root of the function. F(x)= cosx + 2sinx + x^2 to 5 decimal places

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Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: B\ find the root of f(x)=x-x-1, in [1, 2] with 4 decimal places and E-0.009 by using Interval…

A: Given:   fx=x2-x-1 in 1,2

Q: Use all your background to find the integral of the hyperbolic function: 00 sinh ax cosh bx

A: Given: The given integral ∫0∞xnsinhaxcoshbxdx

Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

Q: a) Estimate the length of this arc with the length of the line segment joining the endpoints of the…

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Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

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Q: Use differentials to approximate VI2.3 . b Express your answer as a ±- where a is the nearest…

A: Given 12.33 Using differential to approximate 12.33  Let y=x3=x13dydx=13x-23dy=13x-23dxdy=dx3x23

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: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: b) write an expression for the position in terms of time t, use c (lower case) to denote constant of…

A: a =dv/dt where a is acceleration

Q: A stone, projected vertically upward with initial velocity 112ft/sec, moves according to…

A: Topic = Algebra The maximum height reached by the stone is 196 ft.

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: fx=sin-1x,   a=π12 The value of the function and the value of the derivative can be easily…

Q: 78x Sinx d Show that it is Conv drichlet t. divergent by

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Q: Evaluate the derivative of a mq4.5.png cos (bvx ³) f(x) = a ln sin(cx²) if a = 107, b = 0.5, and c =…

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Q: None Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: The linear approximation to 1 over sqrt(5-x) at x=0 is y=?

A: To find the linear approximation at x = 0 to the function 1/sqrt (5–x).

Q: A target oscillates in a straight line from a fixed point, P, such that after t seconds, its…

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Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

A: The Given initial value problem is: dydx=2y-2x2-3, y(0)=2, h=0.3 To find: y(3) using Euler's…

Q: .Find the estimate for the root of f(x) = sin x+ cos (r+1)-1using Bisection methodx, = 1.5, X=2 with…

A: Solution

Q: use taylors formula to find the cubic approximation to f(x,y)=sin(6x+y) near the origin

A: Given Function,fx, y = sin 6x + y

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

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Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: By differentiation with respect to time, show that the equation x = xi + ut + 1/2 at² describes…

A: Given that, x=xi+ut+12at2. Where, xi is the initial position. u is the initial speed a is the…

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

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Q: I* cos z lim 1³+2

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Q: Q1) Is frgof bounded variation texplain your auswer) x* Sin Sint %3D X =0

A: Ansa; According to the given function. Claim f is differential on x=0 Left Hand Derivative.

Q: The graphs of y = srqt(x) and y = 3 - x2 intersect at one point x = r. Use Newton’s method to…

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Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de Keep at least 2 decimal places accuracy…

A: Given that: ∫14cosxxdx and n=4

Q: Use Secant method with p0 =1, p2 = 1.2 to find the root of f(x)= Inx - cosx that is accurate to…

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Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: Use the Fundamental Theorem to evaluate the definite integral exactl- + y* )dy Enter the exact…

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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: Use the trapezoidal rule with n = 20 subintervals to evaluate I = -5 sin² (√0× t) dt

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Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.