Suppose that f (x) satisfies the following equation (an example of a differential equation): f(x) = f
Question:
f″(x) = −f (x)
(a) Show that f (x)2 + f′(x)2 = f (0)2 + f′(0)2 for all x.
(b) Verify that sin x and cos x satisfy Eq. (1), and deduce that sin2 x + cos2 x = 1.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 84% (13 reviews)
a Let gx fx 2 fx 2 Then gx 2f xfx 2fxfx 2f xfx 2fxf x 0 where we ...View the full answer
Answered By
PALASH JHANWAR
I am a Chartered Accountant with AIR 45 in CA - IPCC. I am a Merit Holder ( B.Com ). The following is my educational details.
PLEASE ACCESS MY RESUME FROM THE FOLLOWING LINK: https://drive.google.com/file/d/1hYR1uch-ff6MRC_cDB07K6VqY9kQ3SFL/view?usp=sharing
3.80+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Calculus questions
-
Suppose that f : R R satisfies f(x + y) = f(x) + f(y) for each x, y R. a) Show that f(nx) = nf(x) for all x R and n Z. b) Prove that f(qx) = qf(x) for all x e R and q Q. c) Prove that f is...
-
Suppose that f : (0, ) R satisfies f(x) - f(y) = f(x/y) for all x, y (0, ) and f(l) = 0. a) Prove that f is continuous on (0, ) if and only if f is continuous at l. b) Prove that f is...
-
Suppose that f: X Y is differentiable at x and its derivative is nonsingular. Suppose further that f has an inverse f-1: Y X that is continuous (i.e., f is a homeomorphism). Then f-1 is...
-
Two popular methods of financial statement analysis are horizontal analysis and vertical analysis. Explain the difference between these two methods. Discuss.
-
The text describes five forces (barriers to entry, customer power, supplier power, alternate sources, and intensity of competition) that affect a firms competitive landscape. Required: a. Describe...
-
Accounting records for Joshs Shopping Bags yield the following data for the year ended May 31, 2012: Inventory, May 31, 2011. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $...
-
In a test of homogeneity, the alternate hypothesis says that the distributions in the rows are the same. In Exercises 68, determine whether the statement is true or false. If the statement is false,...
-
Draw a decision tree depicting the reimbursement policy in Problem 1.
-
Company issued bond with par value $509240, coupon rate of 10%, 10-year term. Bonds were issued at 105. Interest is payable annually, and the straight-line method is used for amortization. Assume...
-
Pathfinder College is a small liberal arts college that wants to improve its admissions process. In particular, too many of its incoming freshmen have failed to graduate for a variety of reasons,...
-
Assume that f exists and f(x) = 0 for all x. Prove that f (x) = mx + b, where m = f(0) and b = f (0).
-
Use Exercise 66 to prove: f (x) = sin x is the unique solution of Eq. (1) such that f (0) = 0 and f(0) = 1; and g(x) = cos x is the unique solution such that g(0) = 1 and g(0) = 0. This result can be...
-
Suncare Corporation installs switching systems and receives its pay in the form of notes receivable. It installed a system for the city of Edson, Alberta, receiving a nine-month, 10 percent, $200,000...
-
The effect of an impulse applied to a SDOF system is to cause a discrete change in displacement. Indicate whether the statement presented is true or false. If true, state why. If false, rewrite the...
-
The convolution integral is the solution to the differential equation governing the motion of a SDOF system with initial conditions equal to zero. Indicate whether the statement presented is true or...
-
The equations are ___________ using mode shape ___________ with respect to ___________ and ___________. Regarding the derivation of modal analysis for an undamped system or a system with proportional...
-
The vector of forces for the right-hand side of the equations defining the principal coordinates is calculated by \(\mathbf{G}=\mathbf{P}^{T} \mathbf{F}\). Indicate whether the statement presented is...
-
The elements of the impedance matrix are the transfer functions \(G_{i, j}(s)\). Indicate whether the statement presented is true or false. If true, state why. If false, rewrite the statement to make...
-
Let Z 2 be an algebraic closure of Z 2 , and let , Z 2 be zeros of x 3 + x 2 + 1 and of x 3 + x 2 + 1, respectively. Using the results of this section, show that Z 2 () = Z 2 ().
-
Linda Lopez opened a beauty studio, Lindas Salon, on January 2, 2011. The salon also sells beauty supplies. In January 2012, Lopez realized she had never filed any tax reports for her business and...
-
Write down the definition of the derivative for general x, and use a law of logs to try to convert the limit into something that looks like the limit at x = 1, as in Exercise 31. Instead of plugging...
-
m(t) = l - t/2. Suppose a population of bacteria grows according to P(t) = 10et. Find the first and second derivative to graph the total mass when the mass per individual m(t) has the following...
-
m(t) = 1 - t. Suppose a population of bacteria grows according to P(t) = 10et. Find the first and second derivative to graph the total mass when the mass per individual m(t) has the following forms....
-
Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z=t....
-
1. What is the difference between invitation to treat and offer? 2. Explain the statement "acceptance must be absolute and unqualified." Question 3 Ali goes to the convenience store to buy a can of...
-
The firm sold one of its fixed assets just as the year ended. Would this imply that operating cash flow for the year was a larger figure, a smaller figure, or would have no effect on its operating...
Study smarter with the SolutionInn App