find the terminal point P(x,y) on the unit circle determined by the given value of t.      t=7pi/4 P(x,y)= (         )

Q: Find the arc length of the graph of the function over the indicated interval. x = (1)/(3)(y2 +…

A: Given x=13y2+232 ,0 ≤ y ≤ 8.

Q: The length function for the curve yz ln(sinx) arc stacting point (,0) cwith

A: The arc-length of the curve y=f(x), a≤x≤b is given by: L=∫ab1+(f'(x))2dx

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find the length of the curve 7 (t) = (3 cos(t), 3 sin(t), 5t) for – 4 <t <1 Give your answer to two…

A:

Q: 2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the…

A:

Q: Find the arc length of the graph of the function over the given interval:

A:

Q: Q. Find the length of the arc of f(x) = ÷(x² + 1), 1< x < 4

A:

Q: 3 The arc length of the portion of the curve y=x2 with 0<x<4 is Osz9.0734 OSx 10.1938 s=7.7868 попe

A: We have to find the arc length of the portion of the curve y=x32 with 0≤x≤4.

Q: Find the length of the curve. x = cos t y = sin t

A:

Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

A:

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: Find the arclength of the curve in the given interval. x = 3 cos? t , y= 3 cost sin t , 0 s<t <t

A: solution is written in below steps.

Q: Find the exact length of the curve y = ln(sec(x)),   0 ≤ x ≤ ?/6

A:

Q: The tangent line to the graph of y = e² at æ = 0 is perpendicular to the tangent line to y = e at æ…

A:

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

A:

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

A:

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: 2. Find the length of the curve 1<t<4. given by r= e'(sin t+cos t), y = e'(cos t-sin t), OS

A:

Q: Find the lengths of the curves x = ln (sec t + tan t) - sin t , y = cos t, 0 … t … pi/3

A: x=lnsect+tant-sint,  y=cost,  0≤t≤π3 Differentiating with respect to t, we get ⇒dxdt=1sect+tantsect…

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

A:

Q: x = e* + e=t Find the exact length of the curve for – 2 <t < 0 y = – 7 – 2t arc-length =

A: We use the formula of arc-length of a parametric curve to answer the given question

Q: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

Q: Let P(cosh t, sinh t) be a point on the unit hyperbola x2 − y2 = 1 in the first quadrant . Show that…

A: Redraw the given figure as shown below.

Q: 10. Circles tangent to the x-axis. Amm. [1+())- [yy +1+(.

A:

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

A:

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Find the length of the curve y = ln (sec x), 0 <I<÷.

A:

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

A:

Q: Find the length of the curve y = ln (sin x),  pai/6&lt;=x&lt;=pai/2.

A: The given curve is,

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

A:

Q: 10. Circles tangent to the x-axis. Amm. (1+() =[yy +1+(

A:

Q: The plane curve represented by x(t) = t – sin(t), y(t) = 9 cos(t), is a cycloid. - (a) Find the…

A: we have to find the equation of the tangent line

Q: Estimate s cose S cos(x) dx using the Trapezoidal Rule and the Midpoint Rule, each with n-4. (Round…

A: The trapezoid rule states the integral of a  function f(x)  over the interval [a,b] can  be…

Q: 10. Circles tangent to the X-axis. Amm. [1 + (y)*]° =[yy +1+(]".

A: Every function can be described through a differential equation. The differential equation defines…

Q: 10. Find the point on the curve r(t) = (12 sin t)i – (12 cos t)j + 5tk at a distance 13 T units…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 x2 + 1 y = y

A: Here we need to find arc length of y from x=0 to x=1

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

Q: Find the arc length of the graph of the function over the given interval.          y = ln x, [1, 5]

A: Given, The function y = ln x in the interval [1, 5].   To find the arclength of the graph of the…

Q: 10 cos 0 and y = 10 sin³ 0, find the total length of the curve swept out by the point If x = (x, y)…

A: We have to point length of curve swept out by the point:

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

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: The objective of the problem is to find the distance traveled by the particle whose position is…

Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

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: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: