Q 35.

Question

In exercise, let

$g_{1} (t) = \sin t, g_{2} (t) = \cos t, g_{3} (t) = 1 - t, f_{1} (x, y) = x^{2} + y^{2}, f_{2} (x, y) = \frac{x^{2}}{y^{2}}, f_{3} (x, y, z) = \frac{x + y}{y + z}, r_{1} (t) = ⟨ 1 + t, t - 1 ⟩, r_{2} (t) = <t, t^{2}, t^{3}>$

Either simplify the specified composition or explain why the composition cannot be formed.

$r_{2} (g_{3} (t))$

Step-by-Step Solution

Verified

Answer

Answer is $<1 - t, {(1 - t)}^{2}, {(1 - t)}^{3}>$

1Step 1. Given information

2Step 2. Explanation

$\begin{array}{rcl} r_{2} (t) & = & <t, t^{2}, t^{3}> \\ g_{3} (t) & = & 1 - t \\ r_{2} (g_{3} (t)) & = & r_{2} (1 - t) \\ = & <1 - t, {(1 - t)}^{2}, {(1 - t)}^{3}> \end{array}$

Q 34.

Q 36.

Other exercises in this chapter

Q 33.

In exercise, letg1(t)=sint, g2(t)=cost, g3(t)=1-t, f1(x,y)=x2+y2,f2(x,y)=x2y2, f3(x,y,z)=x+yy+z,r1(t)=⟨1+t,t-1⟩, r2(t)=t,

View solution

Q 34.

In exercise, letg1(t)=sint, g2(t)=cost, g3(t)=1-t, f1(x,y)=x2+y2,f2(x,y)=x2y2, f3(x,y,z)=x+yy+z,r1(t)=⟨1+t,t-1⟩, r2(t)=t,

View solution

Q 36.

In exercise, letg1(t)=sint, g2(t)=cost, g3(t)=1-t, f1(x,y)=x2+y2,f2(x,y)=x2y2, f3(x,y,z)=x+yy+z,r1(t)=⟨1+t,t-1⟩, r2(t)=t,

View solution

Q 37.

In Exercise, sketch the surface of revolution formed when the given function on the specified interval is revolved around the z-axis and find a function of two

View solution