1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x...

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2.

x = t^2 , y= t ln t

2) Find the arc length of the curve on the given interval.

x = ln t , y = t + 1 , 1 < or equal to t < or equal to 2

3) Find the area of region bounded by the polar curve on the given interval.

r = tan theta , pi/6 < or equal to theta < or equal to pi/3

4) Find the length of the polar curve on the given interval

r = (theta)^2 , 0 < or equal to theta < or equal to pi/2

Last few questions from my math packet, any help would help ! Thank you so much.

Expert Solution

milcah answered 2 years ago

Please show work. 1. Find the derivatives dy/dx and d2y/dx and evaluate them at t =...

Please show work. 1. Find the derivatives dy/dx and d2y/dx and evaluate them at t = 2. x = t2, y = tln t 2. Find the arc length of the curve on the given interval x = ln t, y = t + 1, 1 ≤ t ≤ 2 3. Find the area of region bounded by the polar curve on the given interval. r = tan θ, π/6 ≤ θ ≤ π/3 4. Find the length of the...

Find the series solution of the following equation x(d^2y/dx^2+(1-x)dy/dx+ny=0. where n=0,1,2

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value...

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = et, y = e−t t = 3 dy/dx = d^2y/dx^2 = slope = concavity= ---Select--- concave upward concave downward neither

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the...

d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the initial value problem into a set of two coupled first-order initial value problems and find the exact solution to the differential equatiion

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x =...

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2. Solve with Euler’s explicit method using h = 0.4. Plot the x-y curve according to your solution.

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y...

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y = x^2 sin(x) 4.) y' - 2y = e^2x, y(0) = 2 5.) cos(x)(dy/dx) + ysin(x) = 1, y(pi/4) = 0

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y...

Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y ) × (X × Y ) → R by d ((x1, y1), (x2,y2)) = dx(x1,x2)+dy(y1,y2) Prove that d is a metric on X × Y .

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X...

Suppose (X, dX) and (Y, dY ) are metric spaces. Define d : (X ×Y )×(X × Y ) → R by d((x, y),(a, b)) = dX(x, a) + dY (y, b). Prove d is a metric on X × Y .

Question