Question: Using the Inverse Function Theorem, prove that (arcsin x)' = 1/l - x2 for x (-1, 1) and (arctan x)' = 1/(1 + x2)

Using the Inverse Function Theorem, prove that (arcsin x)' = 1/√l - x2 for x ∈ (-1, 1) and (arctan x)' = 1/(1 + x2) for x ∈ (-∞, ∞).

Step by Step Solution

★★★★★

3.44 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let fx sin x Then fx cos x 0 for x 2 2 and f2 2 1 1 He... 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

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (297).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

Let E = L-1 represent the inverse function of L, where L is defined in Exercise 5.3.7. a) Use the Inverse Function Theorem to show that E is differentiable and strictly increasing on R with E'(x) = E...

Q:

Let E = {(x, y): 0 2t, t > 0} and find a formula for f-1[ (s, t). b) Use the Inverse Function...

Q:

By definition, the inverse sine w = arcsin z is the relation such that sin w = z. The inverse cosine w = arccos z is the relation such that cow w = z. The inverse tangent, inverse cotangent, inverse...

Q:

4. Using the Inverse Function Theorem, prove that (arcsin x)' = 1/v'1 - x2 for x E (-1,1) and (arctanx), = 1/(1 + x2 ) for x E (-00, (0).

Q:

PRINTABLE VERSION Quiz 12 Question 1 Given sec(x) = 7 with 90

Q:

Find the inverse function of f informally. f ( x ) = x2 + 3, x 20 f- 1 ( x) = Verify that f(f-1(x)) = x and f-1(f(x)) = x. f ( f - 1 ( x ) ) = f 2 = + 3 = X f - 1 ( f ( x ) ) = f- 1 = - 3 =...

Q:

Can you solve 5 and 6. U pour email before @buffalo.edu). POD Type format longg at the top of your script file to display more in point when displaying your variables in the Command Window.. Script...

Q:

g'(:1:)= m, where f stew f(m)=9'1(=v)= 1 1 Step 2 x) = 1 1 Step 3 f'(9(w)) = 1 1 Step 4 m = 1 1 Now, find g'(:1:) by differntiating using the quotient rule. 912:) =1 1 Use the inverse function...

Q:

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Q:

3. [-/1 Points] DETAILS LARCALCPRECALC3 11.4.014. Find the derivative of the function. f(x) = arcsin(3x) + arccos(3x) f ' ( x ) = Need Help? Read It 4. [-/1 Points] DETAILS LARCALCPRECALC3...

Q:

Policing the workplace used to mean reminding employees about personal phone calls and making sure that paper clips did not disappear. But with the computer revolution at work that began in the...

Q:

Romero Corporation owns a machine that is fully depreciated but is still being used. How should Romero account for this asset and report it in the financial statements?

Q:

20-4 Why is it advisable to select the best method of operation prior to making a time study of a task?

Q:

(C a s e S t u d y : The Reputation of a Big Mac) Explain how the time and financial requirements involved in obtaining a McDonalds franchise relate to the hiddencharacteristics problem.Why would...

Q:

7. Let s = infnEN(suPk>n Xk) and consider the cases s = 00, s = -00, and s E R.

Q:

4. (a) First prove that infk>n Xk +infk>n Yk ~ infk>n(xk +Yk). (c) By (b), the first and final inequalities ca;;- only be st~ict if neithe~ {xn} nor {Yn} converges.

Q:

2.5 Limits Supremum and Infimum 1. (a) 2,4. (b) -1,1. (c) -1,1. (d) 1/2,1/2. (e) 0,0. (f) 0,00. (g) 00,00.

Q:

Scenario 13-1 The information below applies to the following problem(s). The president of Real Time Inc. has asked you to evaluate the proposed acquisition of a new computer. The computer's price is...

Q:

A stock was selling for $ 2 0 per share a year ago. During the year, it paid no dividend. At the end of the year, its price dropped to $ 1 8 . First, compute the percentage return on the stock. T -...

Q:

The interest earned on a $ 6 0 0 0 investment was $ 2 4 0 . What was the term in months if the interest rate was 6 % ? Select one: A . 8 months B . 7 months C . 1 2 months D . 4 months E . 9 months