Question: (7) Let f(x,y,z) be a three-variable function with coetinuous partial derivatives, and let S be a level surface f(x,y,z)=k. Let (a,b,c) be a point on

(7) Let f(x,y,z) be a three-variable function with coetinuous partial derivatives, and let S be a level surface f(x,y,z)=k. Let (a,b,c) be a point on S. Prove that gradf(a,b,c) is a normal vector of the plane tangent to S at (a,b,c).1

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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 Mathematics Questions!

solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks. 1. [-/1 Points] DETAILS SCALCET9 14.1.004. Let h(x, y) = e (a) Evaluate...

7 If F x y z P x y z i Q x y z j R x y z k is a vector field on R and the partial derivatives of P x y z Q x y z and R x y z all exist then the curl of F is the vector field on R defined by OP y and...

DETAILS 1. [-/1 Points] Math 110 Course Resources - Derivatives Course Packet on average rate of change - Video Tutorial Compute the average rate of change f(x) = - on the interval [4,11]. Average...

Section 4.1: (page 247) Numbers 1, 3, 7-13 odd, 19-23 odd Section 4.2: (page 260) Numbers 1, 5, 13, 19a, 20a Section 4.3: (page 270) Numbers 1-5 odd textbroker.com X Final Exam X X Canvas LMS X...

Let C2 be the oriented curve parametriza r(t)= cost V2 ,sint, - cost V2 ), Osts2 n. Let F( x, y, z) = , and let I2=_ F-dr. [Suggestion: Use Stokes' Theorem and the fact that C 2 is the circle in the...

ANSWER. THESE QUESTIONS AS GIVEN IN THE ATTACHMENT. (a) Use implicit differentiation to compute and where z is defined implicitly by y . cos(I' 2) = 1. [3 marks] (b) Suppose that a function f(r, y)...

textbroker.com X Final Exam Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X C D File | /Users/davidorozco/Downloads/MathG140FinalExam-Summer2023%20(1).pdf Update : Suggested Sites M...

854 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 9. 20. Jessica and I at 2 oh ; h (x , y ) = -, x = 1/2, y = 1712 paths that make a with velocity va 10. "J : f ( x , y , Z ) = xy - 22, x = rcos0,...

D F G K L Hturn Z X C V B N M ) - x In(y?). 1xx(2.3) north. The angle D between magnetic north and true north is called the magnetic declination. Use Figure 10 to determine which of the following...

1 Multivariable functions and vector geometry Due date and time: Wednesday, June 7th at 9:30 AM in lecture Please ensure that you have read and understood the document \"Homework Guidelines" on the...

What is the value of adding outside directors?

XYZ Corp's shares are currently trading at $14 each, but ABC Ltd. is preparing for $20 per share tender offer. XYZ estimates the gain from the merger to be $6 million. What percentage of the merger...

Scenario As the newly appointed manager of a retail clothing store, you're analyzing the store's financial health to plan for the next fiscal year. You're specifically looking at the current assets...

Wangshu puts $40000 in a savings account paying interest rate (2) = 8%. He withdraws the money after 34 months. How much money is in his account using a) the "Greedy Bank" method b) the "Practical"...