🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeStudy Guides420,000US230,000

MATH 200 Study Guide - Midterm Guide: Partial Derivative, Chain Rule, Topographic Map

48 views3 pages

champagneminnow798

15 Nov 2016

School

Drexel University

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Z=f(x,y) means z is a function of x and y. W=f(x,y,z) means w is a function of x,y and z. Multi-variate function: a function f of n variables x1, x2, xn is a rule that assigns a unique real number f(x1, x2,xn) to each point (x1, x2,xn) in some set d in n-dimensional space. Level curves: a topographical map of the curve on an xy plane. (cid:3051)(cid:4666)(cid:1876),(cid:1877)(cid:4667) is the slope of the surface in the x direction at the point (cid:4666)(cid:1876),(cid:1877)(cid:4667) (cid:3052)(cid:4666)(cid:1876),(cid:1877)(cid:4667) is the slope of the surface in the y direction at the point (cid:4666)(cid:1876),(cid:1877)(cid:4667) f(x)x=(cid:3051)(cid:3051)=(cid:2870)/(cid:1876)(cid:2870)= (cid:4672)(cid:3051)(cid:3051)(cid:4673) f(x)y= (cid:3051)(cid:3052)=(cid:2870)/(cid:1877)(cid:1876)=(cid:4672)(cid:3052)(cid:3051)(cid:4673) f(y)x= (cid:3052)(cid:3051)=(cid:2870)/(cid:1876)(cid:1877)=(cid:4672)(cid:3051)(cid:3052)(cid:4673) f(y)y= (cid:3052)(cid:3052)=(cid:2870)/(cid:1877)(cid:2870)=(cid:4672)(cid:3052)(cid:3052)(cid:4673) Let f be a function of two variables. If (cid:3051)(cid:3052) (cid:3052)(cid:3051)are continuous on an open disk, then (cid:3051)(cid:3052) = (cid:3052)(cid:3051)on that disk. Local linear approximation (l(x,y)) is the tangent planes that can be used to. 1) add a variable (ex. f(x,y)= f(x,y,z)=-f(x,y)

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH 200 Study Guide - Final Guide: Cylindrical Coordinate System, Unit Vector, Multiple Integral

champagneminnow798

MATH 200 Lecture Notes - Lecture 1: John Wiley & Sons, Pythagorean Theorem, Cross Product

champagneminnow798

MATH 200 Lecture Notes - Lecture 7: Maxima And Minima, Saddle Point, Multiple Integral

champagneminnow798

Related Questions

Show transcribed image text 1. 0/6 points LarCalc11 13.1.010. [3864 VIA Evaluate the function at the given values of the independent variables. Simplify the results. fx, y) -4 -x2 - 4y2 (a) ro, 0) for (c) f2, 3) (e) x, o Cal 2. 0/2 points LarCalc11 13.1.019.MI. [386 Evaluate the function at the given values of the independent variables. Simplify the results. x, y)- 6x y2 (a) fix + ax, y)-f(x, y) Ay
3. 1 points LarCalc11 13.2 Find the indicated limit by using the limits limfx, y) 2 and im g(x, y)--4 lim 4. O/1 points LarCalci1 13 2 Find the indicated limit by using the limits lim x, y) 3 and lim (x, y) g(x, y)--5 (a, b) lim x, Y) (x, y) (a, b) g(x, y) 5. y1 points LarCalc11 13.3 Explain whether or not the Quotient Rule should be used to find the partial derivative. Do not differentiate. ay x2 51 O Yes, the function is a quotient. O No, y only occurs in the numerator. 6. 0/2 points LarCalc11 13.3 Find both first partial derivatives oz 7. 0/2 points LarCalc11 13.3 Find both first partial derivatives. hx, y) ex+y) h(x, y)
8. /2 points LarCalc11 13.3.031 Find both first partial derivatives. az dx az ay 9. /1 points LarCalc11 13.4.003. Find the total differential. z 3xSy10 dz 10. 0/2 points LarCalc11 13.5.012 Consider the following. (a) Find dw/dt using the appropriate Chain Rule. dw dt (b) Find dw/dt by converting w to a function of t before differentiating. dw dt 11. 0/1 points LarCalc11 13.6.008. Find the directional derivative of the function at P in the direction of v. rx, y) = x3-y3, Rio, 9), v-V2 (1+j)
12. 0/2 points LarCalc11 13.7.017 (a) Find an equation of the tangent plane to the surface at the given point. x+y+z=9, (2, 5, 2) (b) Find a set of symmetric equations for the normal line to the surface at the given point. ox -2y -5-z-2 13. /3 points LarCalc11 13.8.025 Use a computer algebra system to graph the surface and locate any relative extrema and saddle points. (If an an not exist, enter DNE.) -8x x2 y21 relative minimum (x, y, z) - relative maximum (x, y, z) saddle point 14. 0/1 points LarCalci1 13.10.027 Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point. Surface Point Plane: x yz 1 (7,1,1)