A particle is moving in such a way that its velocity v is given by the equation v(t) = cost + sin t. Given that its position at time 0 is s = 3, find the position function, s(t).

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x 2−x−2=2y 2−2y

A: We have to find derivative of curve equation (implicitly).Curve equation is given by:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y2 −3x3y4 =1

A: We have to find  dy/dx of curve equation  (implicitly).Curve equation is given by:

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

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Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: Find the differential of each function. (a) y = tan(7t) dy = 3 - v2 (b) у 3 3 + v2 dy =

A: topic - differential equations

Q: Find the differential of the function. y = 04 sin(120) dy =

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

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Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three…

A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

Q: The equation of the tangent line to the curve y = 1 at the point (3,-) is Vx +1 A. x+16y +11=0 B. x+…

A: Please refer the attached solution. None of the option is correct here . I have solved it…

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: A particle moves along the x-axis with velocity given by v(t) = ; sin (t) for time t > 0. If the…

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Q: Find the equation of the tangent line to y = e¯4t at t = 0.

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Q: Find the value of dy/dx at the point (-2, 1) for the function which is defined implicitly by x²y – -…

A: Differentiate wrt x

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: If the D. E. + M(x, y))dx + sin(xy)dy = 0 is exact then the function М(х, у)

A: If the Differential Equation 1y+M(x,y)dx+sin(xy)dy=0 is exact then the function M(x,y)

Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: Use Euler's method to approximate the indicated function value to 3 decimal places, using h = 0.1.…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

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Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

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: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3+x5y4=−1

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Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x 3− x4 y2 =-2

A: We have to find derivative of curve (implicitly).Curve equation is given by:

Q: Obtain dy from the following function y= e v*

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Q: A particle moves along the x-axis with velocity given by v(t) = 57 sin (t) for time t>0. If the…

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Q: If y = 1+ sin t ,x = cost at t == 2 Find- dt by using Chain Rule, then choose the correct answer:

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Q: Find the derivative, dy/dx of the following using the chain rule: a) y= . . x+1 d) y= 3x+1" f)…

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Q: Find for the equation below. dy dt

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Q: The equation implicitly defines y as a function of t. Find dy dt 1² sin (7 y) = -8

A: This question is based on implicit differentiation.

Q: Assume that x and y are both differentiable functions of t and are related to the equation: y =…

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: (b) f(x)= e²**1 at P (In 2, 4e) 2.x+1 3De

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Q: H.wl: Find L St. sin 2t.dt -3t {e p1 p2

A: We find Laplace transform of given function

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A:

Q: Given a particle is moving in a curve r(t) = cos  7t i + sin 7t j +  8t k. Find the tangential…

A: Given a particle is moving in a curve, r(t) = cos  7t i + sin 7t j +  8t k. To Find the tangential…

Q: x = 6 sin t, y = t +t at t = 0.

A: Let's find.

Q: Find the 3rd derivative of the function given by the parametric equations x=1+t2, y=t−t3 at t=1.

A: Differentiate x and y with respect to t.

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x3+y4=3

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Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

A: integration of velocity funct

Q: Given the function y = x3 + 7x, find the differential dy.

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Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: Given the equation y In (x+y" +9) = 5, evaluate dy Assume that the equation implicitly defines y as…

A: The given equation is  y.ln(x3 + y4 +9) = 5 To find dy/dx

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: the given velocity v(t) = e2ti– sin tk and r(0) = (1,2,0) to find the position at time t = 1.

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Q: Find an equation of the line tangent to the curve at the point corresponding to the value of the…

A: Using formula of equation of tangent line.