2. Prove the following:[r • (r' × r")] = r • (r′ × r").dt3. The binormal vector of a function r(t) is defined as B = T × N, wherer' (t)||r' (t)||is the unit tangent vector andT(t)N(t)==T'(t)||T' (t)||is the unit normal vector.Find the binormal vector for r(t) = (cost, sint, 0).

Note: Since you have posted multiple questions we will solve the first question for you. To get the…

Answered: 2. Prove the following: d dt r. (r [r.…

Math

Calculus

2. Prove the following: d dt r. (r [r. (r' × r")] = r. (r' xr").

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.1: Increasing And Decreasing Functions

Problem 44E: Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line...

See similar textbooks

Related questions

Q: A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $8 the…

Q: F(x) = F'(x)= = 2x 1,²² t² t² + 1 dt

A: Given query is to find the derivative.

Q: Question1: a) Find a power series representation of 1/(3-2x). b) Find a power series…

A: (a) Given that , fx=13-2x Find a power series representation of fx.

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. To be…

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

Q: 4x² - y² 5 (-1, -3) that has a positive a component. For the function f(x, y) = 3 find a unit…

Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

Q: Consider the function f(x) = 2x¹. Determine each of the following.

Q: Find the Taylor polynomials p3 and p4 centered at a=0 for f(x) = (1+x)-³. P3(x) =

A: we will find the required.

Q: If f is differentiable and f(-1)=3; f(-1)=-2, evaluate the following limit lim f(4x-1)-f(x-1)_ X40 X

Q: Express the given equations in polar equations. x² + y² = 7 4xy = 3 (a) (b)

Q: For the given cost function C(x) = 52900 + 300x + x² find: a) The cost at the production level 1000…

Q: Consider the function y= x Find y'.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Given f(x) = x² + 3x + 4, what is 07+h 2x+h+3 Oh+4 Oh² +7h f(2+h)-f(2) h equal to?

Q: Use Newton's method to approximate a root of the equation x³ + x +3 Let 1 = The second approximation…

Q: Question Differentiate the series represented by the function f below term-by-term to find the power…

A: Let's find power series of function derivative f'.

Q: 0 A B (5, 1) C (2y+1,2-y)

Q: vi viii 22 0 TT cos 4x dx sin6x dx

A: Fonding the integrals,use the reduction formula.

Q: 162. y² = 4x For the following exercises, convert the polar equation to rectangular form. 163. r 4…

Q: Calculating First-Order Partial Derivatives In Exercises 1-22, find af/ax and a flav. 15. f(x, y) In…

Q: In the implicit function exy² + x² = 1, y is a function of x. Find an explicit formula for y and…

A: Given function:- exy2+x2=1

Q: 4. Assume that f and g are differentiable functions for which the following is known. f(0) = 1, f(1)…

Q: Let f(x) = 2 sin(x). a.) |f'(x)| ≤| b.) By the Mean Value Theorem, f(a) − f(b)| ≤ la - bl for all a…

Q: The ratio of quarters to dimes in a money bag is 10:17. How many times the number of quarters is the…

A: ratio of quarter to dime 10 : 17 let number of quarter = 10 x number of dimes = 17x total number…

Q: What is the differential equation of the given 2 parameter family of solutions? y = C₁e* + C₂e³x…

A: To find the differential equation of the given two parameters family of solution, we have to take…

Q: Find the Jacobian J of the transformation T(u, v, w) = (4u +4v+w, 4u − 2v+2w, 4u — 4v +2w) = (x, y,…

Q: Find the absolute maximum and minimum of f(x, y) = 2x + 2y within the domain x² + y² ≤ 9. Please…

A: Let's find absolute maximum and minimum by using Lagrange multipliers.

Q: Use the Limit Comparison Test to determine if the series converges.

Q: Use the Integral Test to determine whether the infinite series is convergent. ∞ 7n (n2 +…

A: The given series ∑n=1∞7nn2+135 We have to find the convergent of the series using integral test.

Q: Centerville is located at (9, 0) in the xy-plane, Springfield is at (0, 4), and Shelbyville is at…

A: Let's say Centerville is point A (9, 0) Springfield is B (0, 4) And Shelbyville is C (0, -4) And the…

Q: Given f(x, y) = sin(x + y) where x = f(x(s, t), y(s, t)) = f(x(s, t), y(s, t)) = Question Help:…

A: we need to find out the partial derivatives.

Q: iv 1 S₁²x x³ (1-x)5dx 3

A: The objective of the question is evaluate the definite integral.

Q: What is the differential equation of the given 1 parameter family of solutions? y = In[x + C] O y' =…

A: we need to find out the differential equation for the given equation.

Q: Find the centroid of the lamina bounded by the x- and y-axes, the line x = 2, and the graph of y=e*.…

Q: Optimization problem Steps: 1) sketch 2) label and define the quantities 3) constraint equation 4)…

Q: f(x) = 6e9x³-9x

A: Given find first derivative

Q: Given a nominal interest rate of 1.5% compounded daily (ie: compounded on each calendar day),…

A: Solution- Given Accumulated value after 9 years (A)=$20,000 Rate(r)=1.5% or 0.015 (annually)…

Q: A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $10 the…

A: Given query is to find the ticket price for maximum revenue.

Q: x² dx 2. √√√² +16 2

Q: Solve the equation (1-5x)e¹-5 =0 for x. Give your answer as an integer or a fraction.

A: lne=1lnxn=nlnx

Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy dx 6 +…

A: Givendydx=6+18xxy2 and intial condition y(1)=6We need to find the function y=f(x)

Q: a. Find an equation of the tangent line at x = a. b. Use a graphing utility to graph the curve and…

Q: 2 Weight Gains 12. The graph at the left shows the weight of a baby and the weight of a puppy for…

A: Given graph:-

Q: 3. Find the volume of the portion of the ball x² + y² + z² ≤ 1 lying above the plane z = 3/5. (I…

A: Given that solid is bounded by x2+y2+z2≤ and lying above the plane z=35

Q: Use the ALEKS graphing calculator to solve the equation. sin 3x=-1.2x+1.4 Round to the nearest…

A: Concept: The graph of the sine function is up and down curve which repeats itself after every 2π…

Q: |¸ If f(x) = (2x)², find f(-4). - 2. If f(x) = x² – 3x, find f(−1.8). 3. If f(x) = -2x² + 6, find…

Q: The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is…

A: Given that the concentration of a bloodstream t hours after injection into muscle tissue is given by…

Q: If the derivative of a function is given by f '(x) = x(x - 2)(x + 6), then for what values of x is…

A: Given: f'x=xx-2x+6 To get values of x is fx decreasing put f'x<0 xx-2x+6<0…

Q: You and your friend are shopping at the the nearby Target store. You spent 78 dollars on 3 pounds of…

Q: that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find…

A: Given query is to apply rolle's theorem.

Question

2. Prove the following:
[r • (r' × r")] = r • (r′ × r").
dt
3. The binormal vector of a function r(t) is defined as B = T × N, where
r' (t)
||r' (t)||
is the unit tangent vector and
T(t)
N(t)
=
=
T'(t)
||T' (t)||
is the unit normal vector.
Find the binormal vector for r(t) = (cost, sint, 0).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line horizontal?
4. Find the unit tangent vector T(t) to the curve r(t) = (In(cos t), cost, sin t) at time t. (a) (-sint, -sint cost, cos² t) (b) (-tant, - sint, cost) (c) (sin t, - sint cost, cos² t) (d) (tant, - sint, cost) (e) None of the other choices.
4. Calculate the derivative of the vector-valued function, r(t) = (t')i + (sect)j + (2')k
6. Use a property of derivatives of vector valued functions to show that F(t) x F'(t)] = r(t) x 7"(t)
Find the derivative, r'(t), of the vector function. r(t) = at cos(5t)i + b sin*(t)j + c cos“(t)k r'(t) = Need Help? Read It
Ex.: Find the directional derivative of the function f(x, y) = x'y* + x*y* at the point (1,1) in the direction of the vector (4,3).
Let u(t) = 9t'i+ (² -1)j-6k and v(t)= e'i+5 ej- e k Compute the derivative of the following function. u(t) - v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the vector-valued function i+ k. O B. The derivative is the scalar function Click to select and enter your answer(s) and then click Check Answer. All parts showing Clear All OK earch
Let u(t) = 2t'i+ (P -7)j-8k and v(t) = e'i+3 ej- ek. Compute the derivative of the following function. 3t L u(t) • v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function 訓這 O B. The derivative is the vector-valued function (i+ (Dj+ ( k.