By differentiation with respect to time, show that the equation x = xi + ut + 1/2 at² describes the position of a particle whose initial position is xi and whose initial speed is u moving along the x axis with constant acceleration a

Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: What is the graphical interpretation of instantaneous velocity at a specific time t = to?

A: Instantaneous velocity at a specific time t = to is the slope of the tangent to the curve of…

Q: Show that if acceleration is constant, then the change in velocity isproportional to the length of…

A: Show that if acceleration is constant, then the change in velocity is proportional to the length of…

Q: Find the equation of the tangent line to the curve t(x) 16 4Vx at x = 4 O y=-2x-4 O y=-2x+4 O y=2x+4…

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Q: find an equation of the tangent line at the point indicated. R(z) = log5(2z2 + 7), z = 3

A:

Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: Find the equation of the tangent line to f (x) = ex at x = 2. Give answer in exact form. x²-1

A: Given : fx=exx2-1

Q: Use differentials to approximate the quantity   √17

A:

Q: Find the equation(s) of the tangent line(s) from xy^2-y-2=0 at x=1 (Use implicit differentation)

A: Put x= 1 to find the values of y and then find the equations of tangent.

Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: Find the equation of the tangent line for f (x) = 2 sec(z) at z = 6

A: To find out the equation of tangent line.

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Suppose the tangent line to the curve y = f(x) at the point (1, 1) has the equation y = 5 - 4x. If…

A:

Q: Find the equation of the tangent line to y = arctan(2x) when x = V3 O y - = ( - ) 1 3 O y - = }(2 -…

A: Let's find.

Q: Find the equation of tangent lineto the cubic x^3-6x^2+10x+8 parallel to the line y=x

A:

Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

A:

Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

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Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: By using first principle of differentiation find f'(y), if ƒ(y) = /My – N

A:

Q: 7. Find an equation of the tangent line to the curve y = 1 y = 1+3r IVI that is parallel to

A: The objective is to find the equation of tangent line.

Q: Determine the equation of the line tangent to x² + sin y = xy² +1 at the point (1,0).

A: The equation x2+siny=xy2+1, we have to determine the line of the tangent at the point (1,0).

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Find the derivative. X dt 14) dx lol 0 5t+ 6

A: To find the derivative of given integral.

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: Compute the derivative: 4 te* dt d 3z2 L tet dz -1

A:

Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

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Q: Suppose the tangent line to the curve y = f(x) at the point (1, 1) has the equation y = 9 - 8x. If…

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Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: Find the equation of the tangent line at the given point. 4x = -5xy + 4y at (1,–4) y = arccos(5x) at…

A: See the calculation below

Q: Suppose the line y = 6x - 4 is tangent to the curve y = f(x) when x= 2. If Newton's method is used…

A: According to Newton's method, if the first root is considered to be x1 then the root of the function…

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: The equation of tangent line to y =2rsinx at the point (T) is : Select one: a. y=2x O by=-2x+27 O…

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Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh (;) – ež, find…

A: If the acceleration of the function is a(t) then the velocity of the particle is obtained as…

Q: x =t - sint y = 1- cost

A:

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh () – ež, find…

A: The differentiation of velocity with respect to time is known as acceleration.

Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: Suppose the tangent line to the curve y = f(x) at the point (7,9) has the equation y = -3x + 30. If…

A: