Question: Prove that cosh 1 t = ln(t + t 2 1) for t > 1.

Prove that cosh−1 t = ln(t + √t2 − 1) for t > 1.

Step by Step Solution

★★★★★

3.31 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let t cosh x Then Moreover be... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

Complete the following steps to prove that when the x- and y-coordinates of a point on the hyperbola x 2 - y 2 = 1 are defined as cosh t and sinh t, respectively, where t is twice the area of the...

Q:

The Aggie Watch Corporation manufactures watches on a conveyor belt with 6 stations. One worker stands at each station and performs the following tasks: a . Where in the process is the bottleneck? b...

Q:

Would you accept the project using NPV as your decision criterion? Why or why not? Consider a capital project with the following cash flows: What is the net present value of this project if the...

Q:

Questions 1, 11, 12 Determine whether the improper integral converges or diverges. 11 ) [ 2xe- x 2 dx 11) - 20 A) Converges B) Diverges Find the area or volume. 12) Find the volume of the solid...

Q:

Solution: (a) The concentration of the solution initially is 50 =0.05 kg/ L 1000 (b) Let s(t) denotes the number of kg of salt in the tank after t minutes. Hence, s'(t) would denote the rate at which...

Q:

In questions 1-4, note that ln() represents the natural logarithm (logarithm to the base e) of the expression inside of the parentheses. Below, expand each of the expressions on the right side of the...

Q:

Approximate the solutions to the following elliptic partial differential equations, using Algorithm 12.1: a. 2u / x2 + 2u / y2 = 0, 0

Q:

Mathematics 220 Homework 7 Due March 3/4 1. Question 6.2. Prove that any non-empty subset of a well-ordered set of real numbers is well-ordered. 2. Prove that for all n N 1 1 n 1 + ++ = . 12 23 n(n +...

Q:

Use Direct proof or contrapositive proof to solve and write in paper of each proofs. 1. If m, ne Z, then {xzZ:mn|x} C{xzZ:m|x} n {x=Z:n|x]. 2. If A, B and C are sets, then A U (Bn C) = (AUB) n (AUC)....

Q:

Compute the Leonardo numbers by recursion The Leonardo numbers are a sequence of integers defined as follows: 1 L(n)=1 L(n 1) + L(n 2) + 1 - n = 0 n = 1 n2 Write a static method public static int...

Q:

What is an order of magnitude? Explain why such an estimate can be useful even though it may be as much as 10 times too large or too small.

Q:

Ehrling Brothers Company makes jobs to customer order. During the month of July, the following occurred: a. Materials were purchased on account for $45,670. b. Materials totaling $40,990 were...

Q:

What is the likely impact on a country's exchange rate following an increase in the demand for its exports?

Q:

Financial markets exist, to a greater or lesser degree, to: a. Connect surplus funds with investment opportunities. b. Provide mortgages for homeowners. c. Provide finance for small businesses. d....

Q:

(a) Find the distance from P 1 = (-2, -3) to P 2 = (3, -5). (b) What is the midpoint of the line segment from P 1 to P 2 ? (c) What is the slope of the line containing the points P 1 and P 2 ?

Q:

The variable interest rate on a student loan changes each July 1 based on the bank prime loan rate. For the years 1992-2007, this rate can be approximated by the model r(x) = -0.115x 2 + 1.183x +...

Q:

Find a function H that multiplies a number x by 3, then subtracts the cube of x and divides the result by your age.

Q:

Are the Sternmans required to file Form 982, Reduction of Tax Attributes Due to Discharge of Indebtedness? If so, what is the amount recorded on line 10a of this form?

Q:

Required: Complete the Production Department's Flexible Budget Performance Report

Q:

Solar Shades has 8.6 million shares of common stock outstanding, 4.6 million shares of preferred stock outstanding, and 16 thousand bonds. If the common shares are selling for $13.60 per share, the...