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Chapter 11: Q1P (page 548)

Sketch or computer plot a graph of the function y=e-x2 .

Short Answer

Expert verified

The graph shown is the graph of the function.

Step by step solution

01

Given Information

The value of the function isy=e-x2 .

02

Definition of graph

The graph is a pictorial representation of the function.

03

plot the graph

The value of the function is y=e-x2 .

For x,y=0,1

For x→±∞,y=0

From the coordinates mentioned above plot the graph.

The graph is shown below:

Which is the required graph.

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Most popular questions from this chapter

The following expression occurs in statistical mechanics:

P=n!(np+u)!(nq-u)!pnp+uqnq-u.

Use Stirling’s formula to show that

1P□xnpxynqy2πnpqxy,wherex=1+unp,y=1-unq,p+q=1.

Hint: Show that(np)np+u(nq)nq-u=nnpnp+uqnq-u.

Use a graph of sin2θand the text discussion just before (12.4)to verify the equations (12.4). Note that the area under thesin2θ graph from 0-π2and the area from π2-π are mirror images of each other, and this will be true also for any function ofsin2θ.

The figure is part of a cycloid with parametric equations x=a(θ+sinθ),y=a(1-cosθ) (The graph shown is like Figure 4.4 of Chapter 9 with the origin shifted to P2.) Show that the time for a particle to slide without friction along the curve from (x1, y1) to the origin is given by the differential equation for θ(t) is t=ayg∫01dyy(y1-y).

Hint: Show that the arc length element is ds=2aydy. Evaluate the integral to show that the time is independent of the starting height y1 .

In A uniform solid sphere of density12is floating in water. (Compare Chapter 8, Problem (5.37).) It is pushed down just under water and released. Write the differential equation of motion (neglecting friction) and solve it to obtain the period in terms of K(5-12). Show that this period is approximately 1.16 times the period for small oscillations.

Show that the four answers given in Section 1 for ∫0π2dθcosθ are all correct. Hints: For the beta function result, use(6.4). Then get the gamma function results by using (7.1) and the various Γ function formulas. For the elliptic integral, use the hint of Problem 17 withα=π2.

See all solutions

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