5

# 2. (35 pts) For function f(z,y); define Dif (ro. Yo), where & is a unit vector: (This asks for the definition involving limit_ not "short cut calculational...

## Question

###### 2. (35 pts) For function f(z,y); define Dif (ro. Yo), where & is a unit vector: (This asks for the definition involving limit_ not "short cut calculational formula_ Illustrate with picture, please: What does it mean (in terms of rates of change)Give calculational formula for Daf (Eo; Yo)_Use yOur calculational formula from part to find the rate of change of f(r,y) = Sry? + y? the direction of the vector (3,3} the point (1,y) = (1,2)In what direction will z - f(I,y) = 1 3ry? + y

2. (35 pts) For function f(z,y); define Dif (ro. Yo), where & is a unit vector: (This asks for the definition involving limit_ not "short cut calculational formula_ Illustrate with picture, please: What does it mean (in terms of rates of change) Give calculational formula for Daf (Eo; Yo)_ Use yOur calculational formula from part to find the rate of change of f(r,y) = Sry? + y? the direction of the vector (3,3} the point (1,y) = (1,2) In what direction will z - f(I,y) = 1 3ry? + y' decrease most rapidly at the point (T,y) = (1,2)- Why? Prove that your computational formula in part holds for any unit vector and any differentiable function f

#### Similar Solved Questions

##### 12 Do the set of matrices s-{(: : H: H; ; H; :} form a basis for Mzz? Refer to the definition of a basis for full marks. [5 marks]
12 Do the set of matrices s-{(: : H: H; ; H; :} form a basis for Mzz? Refer to the definition of a basis for full marks. [5 marks]...
##### Random sample of size 10 from normal population has mean 9.45 and standard deviation 2.15 Construct a 90% confidence interval for the population mean 10. A sample of size 10 from normal population has sample variance 9802 = 5.67. Construct &
random sample of size 10 from normal population has mean 9.45 and standard deviation 2.15 Construct a 90% confidence interval for the population mean 10. A sample of size 10 from normal population has sample variance 9802 = 5.67. Construct &...
##### 2. [2Spts] In each week you " 'IL have exactly one problem; which is one of three types A, B or C. The probability that the problem is of type A, B or C is 20%, 30% and 50%, respectively. Judging from your previous experience up to last week in solving the exercise, your probability of getting a right solution is 80% for type A, 40% for type B, and 50% for type C.[IOpts] What is the probability of solving a problem when you get it this week? [1Spts] What is the probability that it is
2. [2Spts] In each week you " 'IL have exactly one problem; which is one of three types A, B or C. The probability that the problem is of type A, B or C is 20%, 30% and 50%, respectively. Judging from your previous experience up to last week in solving the exercise, your probability of ge...
##### Benerally sell In one wcek: Fouteen 2.4 Box Plots asked the number o â‚¬ars they Benerally _ sell (Ive â‚¬ars; nlne randomly selected car salespersons were generally = sell (our cars; twelve Slxty-five generally sell Ghree cars; nlneteen people answered that they generally = sell seven cars, generally. 'sell _ slx cats; eleven ruler (0 measure and scale accurately: out evenly, Ol concenuraled box plot belou: Use concentrated together; - splead = 40. Construct the data are box plot; does It
Benerally sell In one wcek: Fouteen 2.4 Box Plots asked the number o â‚¬ars they Benerally _ sell (Ive â‚¬ars; nlne randomly selected car salespersons were generally = sell (our cars; twelve Slxty-five generally sell Ghree cars; nlneteen people answered that they generally = sell seven cars,...
##### Mini Fdedtities the ~table exact tan value Sla by using the half-angle Incorrect 2+ 1Previous1 and complete JaterDone
mini Fdedtities the ~table exact tan value Sla by using the half-angle Incorrect 2+ 1 Previous 1 and complete Jater Done...
##### (10 points) Find the general solution of the equation9 + (I/t)y = %sin 2t, t > 0
(10 points) Find the general solution of the equation 9 + (I/t)y = %sin 2t, t > 0...
##### The body mass index (BMI) is calculated for random sample of 100 U.S adults The mean BMI for those who were sampled was 27.66 with standard deviation 3,53. Find and interpret an (approximate) 95% confidence interval for the true mean BMI ofU.S adults . When caleulating the contidence interval in a), what assumption did you make about the population from which the data was sampled? A BMI greater than 25 is considered overweight. Would you consider America average BMI as overweight? Explain:
The body mass index (BMI) is calculated for random sample of 100 U.S adults The mean BMI for those who were sampled was 27.66 with standard deviation 3,53. Find and interpret an (approximate) 95% confidence interval for the true mean BMI ofU.S adults . When caleulating the contidence interval in a),...
##### N ( H CH~CH-CH; JId CH,_CH-CnfC CH; CHt cCH, Ch CHFCH a CH ~CH_CH-CH,Write the IUPAC name for each of the following: CHz CH; CH; CHz CH: CH _ CH;- CH;CHz CH;
n ( H CH~CH-CH; JId CH,_CH-CnfC CH; CHt cCH, Ch CHFCH a CH ~CH_CH-CH, Write the IUPAC name for each of the following: CHz CH; CH; CHz CH: CH _ CH;- CH; CHz CH;...
##### Work each exercise. Show that $\tan (-x)=-\tan x$ by writing $\tan (-x)$ as $\frac{\sin (-x)}{\cos (-x)}$ and then using the relationships for $\sin (-x)$ and $\cos (-x)$.
Work each exercise. Show that $\tan (-x)=-\tan x$ by writing $\tan (-x)$ as $\frac{\sin (-x)}{\cos (-x)}$ and then using the relationships for $\sin (-x)$ and $\cos (-x)$....
##### 1. Suppose {X;} are iid ~ Unif(o, 0) . Consider the testHo : 0 = 00 against Hi 0 < 00Use the likelihood ratio test to show that the critical region C has the formC = {(81,_En)lyn < cf}.Find c in term of the significant level & and 0o.
1. Suppose {X;} are iid ~ Unif(o, 0) . Consider the test Ho : 0 = 00 against Hi 0 < 00 Use the likelihood ratio test to show that the critical region C has the form C = {(81,_ En)lyn < cf}. Find c in term of the significant level & and 0o....
##### How many arrangements of answers are possible for a true/false test with 10 questions?
How many arrangements of answers are possible for a true/false test with 10 questions?...
##### For the following function: complete the description, draw the graph, and give possible function_FUNCTIONr-intercepl(s)(-2 0) and (3,0)Y-interceplDomainHole(s)NONEVertical Asym_x =-4 and x =1Horizontal Asym:y = 1Oblique AsymNONEEnd Behavior (use limit nolation)Graph:
For the following function: complete the description, draw the graph, and give possible function_ FUNCTION r-intercepl(s) (-2 0) and (3,0) Y-intercepl Domain Hole(s) NONE Vertical Asym_ x =-4 and x =1 Horizontal Asym: y = 1 Oblique Asym NONE End Behavior (use limit nolation) Graph:...
##### Walmart is purchasing a large quantity of snow pants. Themanufacturer offers a 26/8 chain discount. What is the percentageof discount?
Walmart is purchasing a large quantity of snow pants. The manufacturer offers a 26/8 chain discount. What is the percentage of discount?...
##### 2ALKENEIALKYNE NOMENCLATURE: Provide Syaemilc nuIL for the [ollowing:Br1*:
2ALKENEIALKYNE NOMENCLATURE: Provide Syaemilc nuIL for the [ollowing: Br 1*:...