evaluate-the-given-functions-gr-sr-2-r-s-r2-s-text-find-g-21-text-and-g0-5-3

Question

Evaluate the given functions.
$$g(r, s)=r-2 r s-r^{2} s ; 	ext { find } g(-2,1), 	ext { and } g(0,-5)$$

Tyler Moulton · Accepted Answer

Yeah. We want to evaluate the given functions for the function G e r s equals ar minus two rs minus r squared s. We want to find you have negative to one mg of zero. Negative five. This question is testing our ability to work with both hybrid functions which is a pretty precision multi variable calculus as such. We need to understand that similar to single variable functions. Always due to evaluate these two Gs is by plugging in the indicated numbers for the variables. So forgive negative to one for instance. Well fucking negative to wherever we see our one wherever we see. S so we have you have negative 21 equals negative two minus two times negative two times one minus negative two squared times one or negative two plus forward by this too is zero. Similarly for GM0 to get by we have zero but it&#x27;s two times 0 to 65 minus zero squared 10 95. All over three of our terms have a zero and let&#x27;s go to zero, which means our solution is zero.

James Kiss · Answer

given the function g of T. We want to find We want to evaluate this function for writing inputs the first being G of negative too. To find g of negative two would plug negative two in for tea so it&#x27;ll look like negative too. Plus two over negative too minus two. Well, negative to close to zero and negative two minus two was negative. Four and zero or negative for a zero. Sergey of negative two is zero. Next we have g of positive too. Do you Positive too would be to plus two over to minus two and two plus two is four tu minus 20 But we can divide by zero. This is undefined. So geo to does not exist. We say that you know it is undefined. Next is G of zero. So we put zero in for tea. I would look like zero plus two over zero minus two zero close to is 20 minus two is negative. Two two over. Negative two is negative one. So geo zero is negative. One. Next we have G of a so we substitute tea with a A close to over a minus two. That&#x27;s all for that one. Next, we have G of a squared minus two. So that would look like Hey, squared minus two. Close to over a squared, minus two minus two. Clean it up. Negative. Two plus two is zero. So just a squared in the numerator and a squared minus two minus two is a squared minus four in the last one g of a plus one be equal to a plus one plus two over a plus one minus two A plus, one plus two is the same. Thing is a plus three a plus one. Last year was the same thing Is a minus one? Yeah.

Ankit Gupta · Answer

in this question we have given here Ah, function G p which is equal to d plus two and in denominator d minus two. Okay. And we have to evaluate the function here at the indicated values. That means we have to evaluate the function at different values off. So what is giving here in discussion? We have given her a number called D, and we have applied some Roussel on this number pieces that adding toe and subjecting to from eight to then dividing the terms. Okay, So when we applied this rule on the number T then even get a function which is quite GT here, that means duties or functions on the So we have to find out the value of dysfunction for the different venues off. So, first of four, we have to calculate the value of dysfunction at is equal to minus two. So this say, this is a question for us to, and we have to put P is equal to minus two in this equation. First two. So it will be like this minus two plus two upon minus two minutes toe against the Here in the middle, it will be zero. That means we can say that G minus two will be called a zero now, coming to the next one Riches too. So men report to t is equal to do in this equation. First, it will be two plus two upon to minus toe. So you can see here in the nominee that it will be zero. And when any number contains denominator a zero that will be equal toe in finite. Or we can say that not defined. So g two will be called the Infinite. Now we have to put these equal to zero. To find out the function, it is equal to zero. So it from according to the question first it movie s zero plus two and zero minus two. So the function at these equal to zero will be equal to after simplification here minus one. Okay, now coming to the next value that this G So we have to put t is equal to a in the question first. So the function will be equal. Toe a place to upon a minus. Okay, Now, coming to the next one they have to put in the next value. S T is equal to a square minus two. Okay, so according to that question first, when we put these equal toe a square minus two, it will be like this. And in denominator, it will be a squared minus tu minus toe against the hair. Google began Salau and a function will be equal to G A square minus no is equal to a square. Are born a squared minus school. OK, now coming to the next value, which is given here as a plus one. That means we have to go to musical to a plus one in this equation first. So after putting a plus one in this, a question first it will be like this. A plus one minus two. Okay, now we have to simplify eight. And after simplification because they&#x27;re the function at physical to a plus, one will be equal to a plus tree. And in the nominated will be a minus one. Okay, so we have find out all the values off function and different values off the US first one, WASI minus two, then g to then G zero. Then we have find out here g a. Then we have find out G a square minus two, then we have find out G eight plus one. So all other our lives our find Hill for the different values off, Okay?

Amy Jiang · Answer

Okay, so we will too wrong with the function at the indicated values. So here we have G of two. So that&#x27;s one minus total over one plus two. So that&#x27;s equal to negative 1/3, another through long to G off negative juice. So that&#x27;s one moneys donated to all over one money still, So that&#x27;s equal to three over negative one, which is equal to negative three. And then we have 1/2 here. So that&#x27;s one minus 1/2 over one plus 1/2. So this is equal to a 1/2 over 3/2 to give just that, we have a 1/3, and then we have gov That&#x27;s one minus a over one plus a and then we have one minus a plus one all over one plus U minus one. So here we have a two minus a all over a. And do you evaluated a negative one? It&#x27;s one minus and negative 1/1 minus one. So this here is equal to two of his earl. Well, we have division by several. So this case this term is undefined.

Savannah Payne · Answer

all righty. So we are evaluating functions. And whenever I&#x27;m looking at a problem that has six parts and it&#x27;s evaluating functions, I like to look at it like a little game. So the fastest way for me to set up this game is wherever this tea is, I go ahead and I just put parentheses and I write everything else the same. So parentheses minus two. Over here. This is gonna be parentheses, plus two parentheses, minus two. This one is going to be parentheses, plus two parentheses, minus two. And the reason why I do that is because this is the input value. So in this situation here, instead of putting in T, we&#x27;re gonna put in negative, too. So when I put in negative two now I can see negative two plus two is zero divided by negative four. That when zeros on top, the answer is zero. All right. Coming back here, the new input value is to so now, two is the new input value. Two plus two is 40 to minus 20 when zero is in the bottom of a fraction, it is owned it on end. Okay. You could not divide by zero. All right, it&#x27;s all fun and games until somebody divides by zero. Right, So then let&#x27;s go ahead and plug. Zero in zero plus two is equal to 20 minus two is equal. The negative to two divided by negative, too. Negative one. So now we have, um, analyzed this function with new miracle values. We need to now analyse dysfunction with expressions. Okay. So again, I can cruise across here. Um, if I want to make it a fast little game, open up that parentheses. Put the plus two in the minus two. Because, remember, the only thing that&#x27;s going to change about your function when you&#x27;re setting it up is those values of tea. So over here, there&#x27;s that parentheses, plus two years that parentheses minus to looking at it again. Who here&#x27;s the parentheses plus two and the parentheses minus two. You can see I loved a significantly larger parentheses. Whenever I can see, this value is significantly larger, and I&#x27;m gonna need some space. So in this situation, instead of putting t as the input value, the input value is a So when you look at this, a plus to that simplified a minus two That simplified. So you&#x27;re simplified version of this answer if you want to drop parentheses is a plus two over a minus two. Some professors don&#x27;t mind, and they might even let you box it out right here to say Bingo. This one&#x27;s my answer. Now, when you do have a numerical value that you&#x27;re plugging in with that expression, this is X squared minus two and then excuse me a square minus two. You can see here that you actually have to combine my terms. There&#x27;s nothing to multiply, so the parentheses drop off, but minus two plus two, those guys cancel out. And so what&#x27;s left in the numerator is a squared and then minus two minus two. Well, that&#x27;s negative. For so in the denominator is a squared minus four and so on that when there was a little bit extra work, which is a little more fun than and now, on this last one, we can see again. There&#x27;s a variable and a constant. So we&#x27;re gonna have a little more work. We can actually combine light terms. Um, because you can see one plus two. That&#x27;s gonna be a plus three with this one in this too. And now, if I plug in a plus one now, I&#x27;m looking at one minus +21 minus two is negative one. So that becomes a minus one. And there we have evaluated dysfunction numerically and also with expressions.

James Kiss · Answer

given the function G. We want to evaluate this function with a variety of inputs. The first input is too. So what if I n g of t we? We replace X with two in the function. So it&#x27;s one minus 2/1 plus two one minus two. His one, um, his negative one and one plus two is three. So g of two is negative 1/3. The next one is g of negative. One g of negative one is found by substituting negative one in for acts. So it&#x27;s one minus negative 1/1 plus negative +11 minus negative one. Is that the same as one plus one in one plus in negative. One is the same as one minus 11 plus one is two in one minus +10 But you can&#x27;t divide by zero. So this is undefined. So g of negative warned doesn&#x27;t exist. It is undefined. Moving on G of 1/2 is one minus 1/2 over one plus 1/2 um, was create common denominators. So this would be two halfs my ass 1/2 and then to have plus 1/2 so that we can add fractions together. Tu minus one is 1/2 and then to close one of 3/2. When you divide by a fraction, you multiply by the reciprocal. So this is the same thing as 1/2 times 2/3 which now we can multiply fractions across. One times two is 22 times three is six and 26 can be reduced to 1/3. So g of 1/2 is equal toe. Wait there. G of a is just one minus a over one plus and there was nothing to simplify here. That&#x27;s a nice one. Give a is one minus a over one plus a. And on the next one g of a my ass, one would be one minus a minus one over one plus a minus one. Distribute the negative. You get one minus a plus one in one plus a minus one one plus one is two minus a over the ones. Cancel a. So guia a minus one is equal to minus a over a In the last one G of X squared minus one is one minus X squared minus 1/1 plus X squared minus one. Distribute the negative one minus X squared plus 1/1 plus X squared minus one one plus one is two minus X squared over the ones. Cancel just X squared G of expert minus one is equal to two minus X squared over X squared.

Problem

Evaluate the given functions. $$f(r, \theta)=2 r(…

Problem 11 Easy Difficulty

Evaluate the given functions.
$$g(r, s)=r-2 r s-r^{2} s ; \text { find } g(-2,1), \text { and } g(0,-5)$$

Answer

$g(2,-1)=10 ; g(0,-5)=0$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 3 Educators

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

Calculus 3 Courses

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 29

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

Vectors Intro

Vector Basics - Example 1

Additional Mathematics Questions

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$g(2,-1)=10 ; g(0,-5)=0$

Basic Technical Mathematics with Calculus

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

Vectors Intro

Vector Basics - Example 1

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Lily A.

Anna Marie V.

Kayleah T.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus