r(t) = (cost, sin t,In (cos t)) from t = 0 to t= %3D (5) Find the length of the curve

Q: Find the exact length of the curve. y = ln(Sec x),   0≤ x ≤ π/4

A:

Q: Find the point at which the curve Sx=t-4 ly=t-4t has a horizontal tangent. (x, y) = |

A:

Q: The slope of the tangent line to the curve x = t cost and y = t sin t at the point corresponding to…

A: The slope of tangent line

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

A:

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: 2. Consider y = cos(2x). 2.1. Find Y dx 2.2. Determine an equation for the tangent line at x 0.

A:

Q: dy of the function y = sec dx (1+ V4 + sin" (4 + z²). Find the derivative 山心

A:

Q: f(x)=x2+2  at (1,2)   Find the equation of the tangent line using delta method

A:

Q: The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where…

A: Given, The tangent line to the graph of y=ln(2x) is perpendicular to x+4y=1 Here, y=ln(2x) To find…

Q: Find an equation forbthe tangent line at t=1 for r(t) with r(t)=(t^3-t,sin(t-1),ln(t))

A:

Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

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

A:

Q: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

A:

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

A:

Q: Find an equation for the line tangent to the curve x= 2sin(t), y= 4cos(t) at the point defined by…

A:

Q: &y dy :5 cos t, the third order derivative dt For the function dt3 is 5 cos t -5 cos t -5 sin t cost

A: Here we will find 3rd order derivative

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: Find the slope of the tangent to the curve y = sin x sinx at x= O a) -1 O b) 1 Oc) 2 d) 0

A: Given : y = xsinx,     at  x=π2

Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

A:

Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13π units along…

A: The smooth curve is rt=12sinti-12cost j+5t k at a distance L of 13π units a curve from point…

Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

A:

Q: Find an equation of the tangent line of y = e" cos T, at z= 0.

A:

Q: dy is maximum for the function, dt Give the coordinates of the point where y = sin(t)- t

A:

Q: 5.) Find and d²y , and find the slope and concavity(if possible) at the given value of the dx2 dx…

A: Given Find out the derivative dy/dx using formula

Q: Find the equation of the tangent to the curve at t = 0

A:

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: Sketch the curve. And indicate the direction of increasing T at T =0

A:

Q: dy For the function dt d°y order derivative = 4 cos t, the third is dt3 -4 sin t -4 cos t 4 sin t -4…

A: Differentiate the given function expression with respect to t twice to find the required value

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

A:

Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

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

A:

Q: ind the derivative dy/dx of the function x=arctanet, y=1+e2t at t=0.

A:

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 < t < π   For which values of t is…

A:

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

A:

Q: Find the point on the curve z = 5 sin(t), y = cos(t), - sts. closest to the point (2,0) . (Hint:…

A:

Q: Find the length of the curve  y = 4 ln(cos(x/4)) from x = pi/2 to pi

A:

Q: dy Find the derivative for the function x = sin 2t, y = – cos t at the point t = dx 6.

A: Using derivatives of parametric equations.

Q: Find the slope of the tangent line to the path of a carnival ride x 7 cos() + sin(7t), y = 7 sin() +…

A: Given  x=7cos(t)+sin(7t) y=7sin(t)+cos(7t) We need to find the slope of tangent at t=0

Q: H.W: Use the chain rule to find the derivative of w = x² + y² with dw respect to t dt with x = cos1…

A:

Q: Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the…

A: use differentiation for finding the equation of tangent line.

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: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

A:

Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

A:

Q: dy Using the product rule for the dx function y = e3" sin x is equal to

A:

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

A:

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: For the smooth curve, find any points where the tangent line is either horizontal or vertical. x(t)…

A:

Q: dw b) If w = (x + tanx). (Vx – 1), and x = tan (cost) find dt

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.