1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

Q: Find the slope of the line tangent to the polar curve at the given point. 9 11. r= 9 sin 0; 2' 6 dy…

A: The given polar curve,r=9 sin θ; -92,11π6

Q: 18. Find the second derivative of y with respect to x of the following parametric equations. x = 1 +…

A: Using derivatives of parametric equations.

Q: 2. Write an integral expression to represent the length of the path described by the parametric…

A:

Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

A:

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

A:

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

A:

Q: Find the parametric equations for the tangent line to the curve æ = t3 – 1,y = to +1, z = t° at the…

A: Find the tangent vector r't:                 r(t)=(t3-1)i +(t5+1)j +t5k Differentiate r(t):…

Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

A:

Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: x(t) y(t) = 3 sin t 8 cos t 0<t< 2n a) What does the curve described by these parametric equations…

A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

Q: (iii) Given the curve with parametric equation x = e and y = In(2-r²) Find the equation of the…

A: Formula: The normal line of the parametric equation x=ft and y=gt at the point t=t0 is the line…

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

A:

Q: 1 cos(t) - 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

A:

Q: 1 For the following parametric equation x(t) = tan t and y(t) = sec t find the tangent line passing…

A:

Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

A:

Q: 8. Find the positive constant a(> 0) so that the parametric equation: x = at, y = -t? is a solution…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

A:

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

A:

Q: Find the slope of the line tangent to the polar curve at the given point. 3 7n 2' 6 r= 3 sin 0; dy…

A: Compute the slope of the line tangent to the polar curve as follows.

Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

A:

Q: 8. Find the positive constant a(> 0) so that the parametric x = at, y = -t? is a solution to y =…

A:

Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

A:

Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Parametric equations for a line:

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

A:

Q: 3. Find the second derivative for the following set of parametric equations a. x = sqrt(t) , y = 2t…

A: We have to find te second derivative.

Q: (b) Find the slope of the line tangent to the polar curve r = 1- 2 cos e at the point where e = -2.…

A:

Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

Q: 1.5 3-X Evaluate the integral *dy dx using polar coordinate

A: Follow the procedure given below.

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: 1.Given x=3( θ-sin θ) and   y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx c. Find…

A: Givenx=3(θ-sinθ)y=3(1-cosθ)To find1)Trace of parametric curve2) dydx

Q: 5. Express the curve by an equation in x and y. x(t) = 2- sin(t) y(t) = cos(t) a. (x-2)² + y² =1 b.…

A:

Q: (0, 0) With an initlai (in meters) of the projectile after t seconds is given by the following…

A:

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: 3. Which of the following is the equation of the tangent () line to the polar curver = sec at the…

A:

Q: (* = 8 cos(t) y = 7 sin(t) Find the exact slope of the tangent line to the parametric curve at the…

A:

Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: Q2: Find parametric equations of the line tangent to the graph of r(1) at the point where t= to.…

A:

Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A:

Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

A:

Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem