Given t2 – 1 - f(x) = dt 1+ cos?(t) At what value of x does the local max of f(x) occur?

Q: Solve the initial value problem dx 2x cos(4t) - dt with x(0) = 1. x(t) = = sqrt(-1/4sin(4t)+1) Hint:…

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Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Solve the initial-value problem for y as a function of x. (16 – x)- dy = 1, y(0) = 5 dx ((1 - D- -…

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Q: Estimate the instantaneous rate of change of f(x)= cos(x-7)+4 at x = π. a) 4. Ax =4 b) Af =1 Ax Oc)…

A: Given function is F(x)=cos(x-pi)+4 where x=pi We are going to find the instantaneous change of this…

Q: Construct a first-order linear ordinary differential equation so that all solutions are asymptotic…

A: Given the function                     f(t)=1+t+t2

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1)- = 3, x(2) = 0 dt

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Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

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Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

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Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: Solve the initial value problems for x as a functionof t. (t + 1) dx/dt = x2 + 1 (t > -1), x(0) =…

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Q: Solve the initial value problem (dx/dt)+2x=cos(4t) with x(0)=−2. x(t)=?

A: Solve the initial value problem

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

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Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: 15. Find the derivative of each of the following functions. TE-2 dt (a) f(x) = /" eV7t-2 %3| (b)…

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Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

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Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1) - 3, г (2) — 0 dt

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Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: What is the first derivative of s(r) = log, sin z 712+8z+2 Provide your answer below: s'(x) =]

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Q: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: Find F'(x). 2x F(x) = cos(t*) dt

A: If f(x) is continuous over an interval [a, b], and the function  F(x) = ∫au(x)f(t) dt then F'(x) =…

Q: Solve the initial value problem dx 2x = cos(4t) dt with x(0) = 1. x(t) = sqrt(-1/4sin(4t)+1)

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Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

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Q: The differential operator D4 annihilates the functions

A: we have to find the functions which are annihilated by the differential operator D4…

Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

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Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: Solve the initial value problems for x as a functionof t. (t2 - 3t + 2) dx/dt = 1 (t > 2), x(3) =…

A: Solution: Consider the given initial value problem is t2-3t+2dxdt = 1  (t>2) Now, separating the…

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Solve the initial-value problem for x as a function of t. (2t³ − 2t² + t − 1) = 0 dx dt = 3, x(2) =

A: Given differential equation is 2t3-2t2+t-1dxdt=3, x2=0. The given differential equation can be…

Q: 3 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given data is : dxdt=5et-3 , x0=4 To find the antiderivative

Q: Find the third order derivative of y = In(cos(2x)). A. y' = -40sec? (2x)tan(2x) B. y' = -80sec?…

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Q: Solve the initial-value problem for y as a function of x. (25−x^2)dy/dx=1, y(0)=9 y=?

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