Question
a. Inscribe a regular n-sided polygon inside a circle of radius 1 and compute the area
of one of the n congruent triangles formed by drawing radii to the vertices of the
polygon.
b. Compute the limit of the area of the inscribed polygon as n → 0.
c. Repeat the computations in parts (a) and (b) for a circle of radius r.
Expand
Transcribed Image Text

a. Inscribe a regular n-sided polygon inside a circle of radius 1 and compute the area of one of the n congruent triangles formed by drawing radii to the vertices of the polygon. b. Compute the limit of the area of the inscribed polygon as n → 0. c. Repeat the computations in parts (a) and (b) for a circle of radius r.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: sin sin %3D

A: Click to see the answer

Q: Consider the functions below. "х F(x) = f(t) dt 2 + u4 f(t) du %3D Find F"(2).

A: We use the fundamental theorem of calculus to find F'(x)  

Q: S V5x – 3 dx

A: Click to see the answer

Q: Suppose that f is invertible, f'(x) is continuous, and that f and f' satisfy the following. 8 f(x) 2...

A: a) We use the fundamental theorem of calculus  

Q: 1. Determine if the following statements are true or false. If it is false, explain why. (a) fesle) ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find the Taylor polynomials po. P1, P2 and p3 for f(x) = at x = 1.

A: Click to see the answer

Q: A particle moves in a straight line with acceleration a(t) = 3t2 + et, initial velocity v(0) = 4

A: Click to see the answer

Q: Find a power series for the function, centered at c. f(x) 3x + 2' f(x) Σ Determine the interval of c...

A: Click to see the answer

Q: Find f. f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 5

A: On integrating, we get

Q: A company estimates that the marginal cost (in dollars per item) of producing x items is 1.84 − 0.00...

A: Marginal cost is the derivative of total cost.  Therefore total cost C(x) can be obtained by integra...

Q: Solve the Attachment problem?

A: Click to see the answer

Q: Let f(1) = 2 and "(1) = 3. Suppose g(a) = f(a)]. Calculate g(1). %3D

A: Click to see the answer

Q: Determine a power series representation for the function. Determine its interval and radius of conve...

A: Click to see the answer

Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second poli...

A: Click to see the answer

Q: company estimates that it will sell N(x) units of a product after spending x thousand dollars on adv...

A: Click to see the answer

Q: Use the shell method to write and evaluate the integral that gives the volume of the solid generated...

A: The radius of the region= y  Height of the region = x= 16-y2 y is from 0 to 4 (from the graph)  

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate cach integral. y ...

A: Click to see the answer

Q: Write Va dx as the limit of Riemann sums with equal length subintervals using RIGHT ENDPOINTS as sam...

A: Click to see the answer

Q: A company that makes thing-a-ma-bobs has a start up cost of $43764. It costs the company $3.35 to ma...

A: Click to see the answer

Q: dx (x-2)

A: Click to see the answer

Q: Question 9 from the attached image.  Thank you in advance.

A: To find the area of region bounded by below curves.

Q: Let ƒ be a function that is twice differentiable for all real numbers. The table below gives values ...

A: Click to see the answer

Q: A tank has the shape of an inverted circular cone with a radius of 4 feet and a height of 6 feet. if...

A: Click to see the answer

Q: Joanne sells silk screened tshirt at community festivals and craft fairs. Her marginal cost to produ...

A: (a)  Consider the linear relationship for the cost function. Find the fixed cost FC using the margin...

Q: Determine all critical points for the function. f(x) = x - 12x + 5 O A. x= -2, x = 0, and x = 2 O B....

A: f(x) = x3 - 12x + 5  

Q: When we estimate distances from velocity data, it is sometimes necessary to use times  t0, t1, t2, t...

A: Click to see the answer

Q: What number a>0 makes it that the area under the function f(x)=sin(2x) between x=0 and x=a is 1

A: The area under f(x) and between x=0 and x=a is given by: Given that this equals 1.  We have to solv...

Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's equa...

A: Click to see the answer

Q: Determine the interval and radius of convergence.

A: Click to see the answer

Q: Find the domain of f (x, y) = x + Y

A: Given function

Q: h of the curve. spiral r = 502, 0s 0 < 2/3 720 3 3)(72+1)3/2-1) 40 280 D) 3. 8075

A: Given curve is Now, length of given curve is

Q: 37. 2(cos x)-/2 sin x dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st quest...

Q: Find the arc length of the cardioid r = 3−3 cos θ.

A: The equation of cardioid is r = 3 – 3cos theta.   The arc length of the cardioid is:  

Q: Find all values x= a where the function is discontinuous 1x2

A: Given Since g(x) is a branch function then the possible point where the function may be discontinuo...

Q: ied region. on r = 4 + 2 sin e B) 367 - 16 4) C) 187 D) 367

A: Click to see the answer

Q: For the function below, find a) the critical numbers b) the open intervals where the function is inc...

A: To find the critical points and intervals where the function is increasing and decreasing of below f...

Q: Find the standard form of the equation of the parabola with the given characteristics.

A: Click to see the answer

Q: The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately R(x...

A: Click to see the answer

Q: [2 0 2 10-8 |2. You are given a system |0 3 Show that the determinant of the coefficient matrix is n...

A: Given equation is

Q: Find the indefinite integral: csc(x)/[csc(x)-sin(x)]dx

A: Click to see the answer

Q: Find f such that the given conditions are satisfied, rx)=x-8, f(3)= 14

A: Given