Math

CalculusQ&A LibraryFind the gradient vector and level curve of the following functions at the given point and show that the gradient is perpendicular to the level curve through the point. a) f(x,y) = x; (2,3) b) f(x,y) = x2+y2; (2,1) c) f(x,y) = x2-y; (2,1) I've already found the gradient vectors and level curves of all of them and also know that to be perpendicular to each-other, their dot product have to be zero, but I cannot find out how to prove that the dot product is zero. Thank you!Start your trial now! First week only $4.99!*arrow_forward*

Question

Find the gradient vector and level curve of the following functions at the given point and show that the gradient is perpendicular to the level curve through the point.

a) f(x,y) = x; (2,3)

b) f(x,y) = x^{2}+y^{2}; (2,1)

c) f(x,y) = x^{2}-y; (2,1)

I've already found the gradient vectors and level curves of all of them and also know that to be perpendicular to each-other, their dot product have to be zero, but I cannot find out how to prove that the dot product is zero.

Thank you!

1 Rating

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: please answer question 19

A: Consider a function f(x)=2x+cosxWhen 2x+cosx=0 then f(x)=0f(x)=0 occurs at x intercept.

Q: please answer question 15 with graph

A: The given function is,

Q: As the limit apporaches infinity, find the limit of (8sinx+7cosx)/(x).

A: Given limit function

Q: Find the radian measures that correspond to the degree measures 260° and −155°. (I really just need ...

A: Click to see the answer

Q: Evaluate the integral -2t sin(-3t) dt Note: Use an upper-case "C" for the constant of integration.

A: Given Integral;

Q: Can you help me step by step?

A: The function is given by

Q: To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x3 - x, a = 0, ...

A: Given,

Q: If f(3) = 14 and f '(x) ≥ 2 for 3 ≤ x ≤ 5, how small can f(5) possibly be?

A: The given conditions are,

Q: Can you help me with this problem step by step?

A: Consider the given derivative function.

Q: Sketch the graph of a functionf having the following characteristics f(2) f(4) 0 f(x)0 if x > 3 f(3)...

A: First point represents the the x-intercepts. Second and fourth point is telling that the graph is in...

Q: Explain how you would solve the following equation: ln ( x ) + ln ( x − 5 ) = ln ( 21 − x ) De...

A: By using the property of logarithms, simplify the LHS

Q: 49. Let f(t) be the temperature at time t where you live and suppose that at time t 3 you feel uncom...

A: a) f'(3)=2, f"(3)=4f'(3) > 0 , so the temperature f(t) is increasing at x=3f"(3)>0 implies at...

Q: Answer the following questions about the function whose derivative is f′(x)=(x-6)^2(x+7). Assume the...

A: Given,

Q: Differentiate the function T(z) = 2z log2 z.

A: The given function is,

Q: I am studying for a precalculus exam and I am stuck on this problem and would like help. Question...

A: Given equation is

Q: 1 0 -1 1. For what values of x does the function f have a local maximum on (0,8)? Answer (separate b...

A: Functions can have "hills and valleys": places where they reach a minimum or maximum value. It may n...

Q: Evaluate the integral x cos(3x) dx Note: Use an upper-case "C" for the constant of integration

A: Given:

Q: Express -x 2dx as aumit X eSS OF ngnt -hard Riemann Sums las the definition Of the indlefmite T cuva...

A: Given integral

Q: Find the following indefinite integrals. X dx= Vx6 +C

A: Given,

Q: 8. In 1950, the world population was 2560 million people. In 1960, the population was 3040 million p...

A: Consider P(t) is the population in the year t.

Q: Optimization: You and your classmates have decided to enter an ice sculpting contest. Before you beg...

A: Given an ice block with the following conditions,

Q: As viewed from above, a swimming pool has the shape of the ellipse x^2/4900+y^2/2500=1 where x and y...

A: To determine the volume of the three dimensional region R , defined by the pool

Q: f(5+h)-f(5) Let f(x)= x2-25. Simplify or evaluate the expression

A: Given:

Q: find the absolute extrema for f(x) = x^2/3 (2-x) on [-1,2] please show all work

A: To calculate the critical extreme values for the given function over the given interval

Q: Calculus Question

A: To check the concavity of a given function f(x) first we need to find the f ''(x).If the value of f ...

Q: 64. Suppose that 3f(x)5 for all values of x. Show that 18 <f(8)- f(2) 30

A: We will make use of Mean Value Theorem. 3 ≤ f'(x) ≤ 5This implies:The function f(x) is continuous an...

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

Q: I am very confused about this chapter and specifically on how the homework is breaking the problems ...

A: Given sequence is

Q: Find the derivative of the function below

A: Given,

Q: see attachment

A: Click to see the answer

Q: Find positive numbers x and y satisfying the equation xy=15 such that the sum 3x+y is as small as po...

A: Click to see the answer

Q: Please answer question d, for h(x) = 5x^3 - 3x^5

A: Using Wolfram alpha the graph of the function is as shown below

Q: Calculate the double integrals 1. R xedxdy, R-[0,1]X[0,1]

A: To find the below double integral.

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) e9x e~x (a) Find the int...

A: NOTE: As you have posted a question with multiple subparts, we will answer the first subpart as per ...

Q: Find an equation of the tangent line to the graph of y = ln(x2) at the point (5, ln(25)).

A: To determine the equation of tangent line at given point.

Q: Let f (x) = x1/3(8x + 12)2/3. Find f ' (x) and the critical numbers for f.f ' (x) = (Ax+B)/3x^c(8x...

A: Use product rule to find the derivative. Use chain rule for (8x+12).

Q: How do you find an equation of a line given a pair of points? EX: (22,26), (4,8)

A: Finding an equation of a line by giving two points

Q: An automobile starts from rest and travels down a straight section of road. The distance s (in feet)...

A: The distance s (in feet) of the car from the starting position after t seconds is given by

Q: Find the maximum and minimum values of the function y = 4 cos(0) 7 sin(e) on the interval [0, 2x] by...

A: Compute the critical points as follows.

Q: Calculus Question

A: Substitute the term with x+h for expression in f(x+h) and x for f(x). Expand the terms and cancel o...

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: The given integral is,

Q: A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y=16-...

A: Please see the white board. The rectangle is represented by the green line.The inverted parabola is ...

Q: The height (in feet) of a certain kind of tree is approximated by h(t)= 120/1+180e-.34t where t is t...

A: The height of a tree in feet as a function of time t in years is as follow:

Q: Can you help with this problem step by step?

A: Given, function is

Q: see attachment

A: For a function of the form y=A sin(B(x+C))+D, amplitude is A, period is 2pi/B,phase shift is C.So we...

Q: Can you help with this problem step by step?

A: Given,

Q: Find f "(x). f(x) = x/x^2 -1

A: Find f’’(x)

Q: Make an appropriate substitution and then use integration by parts to evaluate the integral. dx e

A: Click to see the answer

Q: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a...

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of...

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to...

A: Compute the slope as follows.