Calculus: Existence of Global Maximum and Global Minimum for $f(x)=e^xcdot X^3$

HINT.- $f'(x)=e^xx^2(x3)=0Rightarrow x=0,-3,-infty$ and $f'(x)gt0$ for $xgt0$. You can deduce from this that a global minimum is taken at $x=-3$ and that there is not a global maximum (or it is $infty$ if you want)

1. How to calculate $iint_SF cdot n dS$ for the following.

You should note that for your parameterisation $ vecr(alpha, beta)$, we have that $$ iint mathbfF cdot hatmathbfn text dS = iint mathbfF cdot underbrace dfracleft( dfracpartial rpartial alpha times dfracpartial rpartial beta

ight) left| dfracpartial rpartial alpha times dfracpartial rpartial beta

ight|_= mathbfhatn overbrace left| dfracpartial rpartial alpha times dfracpartial rpartial beta

ight| text dalpha text dbeta ^= text dS$$

2. Prove that $A_T= frac12a cdot b cdot sin(gamma)= frac12a cdot c cdot sin(beta)=frac12b cdot c cdot sin(alpha)$

Hint:note that:$bsin gamma$ is the height with respect the side $a$$asin beta$ is the height with respect the side $c$$csin alpha$ is the height with respect the side $b$From the figure:If $a$ is the basis than $AD$ is the relative heigt and the trisangle $ADC$ is rectangle in $D$ and $AD= b sin gamma$, so the area of $ABC$ is $Area=frac12ab sin gamma$.You can do the same using the oter sides as a basis

3. Is there a general result that groups of order $2^ncdot 3$ are solvable?

Let $G$ be a group of order $2^ncdot 3$. If $G$ has a normal Sylow 2-group, you are done (can you see why?). Otherwise, $G$ has 3 Sylow 2-subgroups, and that gives a non-trivial homomorphism of $G$ to $S_3$ via the conjugation action on these Sylow 2-subgroups. The kernel is a 2-group, and the image is solvable, so again, you are done.

4. Does $kcdot x

Oh, well, I got to this counter-example :$k = 2, x = -2, y=-2$

5. Solve $Acdot x = b$ by Naïve Gaussian elimination

The matrix $A$ is lower triangular and invertible, because all coefficients on the diagonal are nonzero. So when you do the $LU$ decomposition, you have $L=A$ and $U$ is the identity matrix.If you properly do Gaussian elimination, the first step (eliminating under the first pivot) will give the matrix $$ beginbmatrix 1 & 0 & 0 & 0 0 & 1 & 0 & 0 0 & 3 & 1 & 0 0 &-2 & 1 & 1 endbmatrix $$ and so on for the other columns.Since the original matrix has been changed, here's what can be said; after elimination according to the Gauss-Doolittle method (no reduction of pivots), we find, for the augmented matrix, the reduced form $$ [Umid c]=left[beginarraycccc|c 4 & 2 & -5 & 1 & -1 0 & 4 & -1 & 9 & -3 0 & 0 & 6 & -1 & 4 0 & 0 & 0 & 5 & 10 endarray

ight] $$ and the matrix $L$ such that $L[,Umid c,]=[,Amid b,]$ is $$ L=beginbmatrix 1 & 0 & 0 & 0 -2 & 1 & 0 & 0 -6 & -3 & 1 & 0 8 & 2 & -1 & 1 endbmatrix. $$The question 'How is the $U$ matrix related to the reduced terms in the augmented matrix before back-substitution?' is not really clear. What I can say is that the system $$ Ux=c, $$ where $c$ denotes the last column in the reduced augmented matrix, is equivalent to the original linear system $Ax=b$. In particular, the form of $U$ tells you that the system has a unique solution. The fact that $L[,Umid c,]=[,Amid b,]$ implies that $Lc=b$, so $c=L^-1b$.What can be done now is to multiply the last row by $1/5$ and do "backwards elimination", reducing the pivots: we find $$left[beginarraycccc|c 1 & 0 & 0 & 0 & 12 0 & 1 & 0 & 0 & -5 0 & 0 & 1 & 0 & 1 0 & 0 & 0 & 1 & 2 endarray

ight] $$ which shows the unique solution.

6. Show that ($ell^1$, $|cdot|_1$) is complete

Consider a Cauchy sequence $x^n$in $l_1$. Where $x^n = (x_1^n, x_2^n, dots)$. For any $epsilon >0$ there exist $k_1 in mathbbN $ s.t. $|x^p - x^q|_1 k_1$. So $sum_i=1^infty |x_i^p -x_i^q|

추천 기사
What Are Araya Rims Made of? Should I Replace Them?
Um from experience new 700c wheels have curve in the rim wall so the tire bead stay even at high pressure .but that nice vintage aray rim wall has no curve in the rime because it was not designed for high pressure tires . Old rims mostly was disigned for low pressure gumwall tire for a comfortable ride . In the bicycle world the old bouncy steel smooth tire 10 speed was considered a Cadillac because of its smooth ride.^,^1. Have any experiments been performed on the magnetic properties of neodymium at high pressure and temperature?Do not think that pure Nd is ferromagnetic (maybe it's antiferromagnetic?), so your question about the Curie temperature really applies to just certain ferromagnetic alloys of Nd. Not aware of any high-P studies on those ferromagnetic alloys offhand. I was a co-author of a paper that looked at the magnetic properties of the heavy lanthanides (which are ferromagnetic) under pressure, and we found that their Curie temperatures dropped with pressure at a $dT_c/dP$ rate of around -10 to -20 K/GPa (See High-pressure magnetic susceptibility experiments on the heavy lanthanides Gd, Tb, Dy, Ho, Er, and Tm). If Nd alloys have $T_c's$ which drop at similar rates, then I would not expect any magnetism in them at the pressure and temperature of the core-mantle boundary (140 GPa and 5000 C)2. 3 ton tempstar heatpump with a 3.5 ton airhandler on a 45 deg, day what should the low and high pressure be?I very much doubt a setting done by a technician charging a system such as yours. First, you cannot do that with two gages. Its not even possible, and second there is NO exact pressure setting for a given system. It depends on air pressure, humidity and relative humidity to set the charge of gas correctly which would result in a "correct pressure " reading. The method most commonly used is a "super heat" method. Here a sling is swirled thru the air and the RH of the air is determined. Next, the exit air from the air blower inside the house is determined. Along with the outside and inside air temps. Then and only then, a chart inside the cabinet of the AC or heat pump is read to find the correct charge pressure. Without taking any of these needed measurements, no pressure reading can be determined. What is happening nation wide is the charging of these new high efficiency units is being done incorrectly, and given that the efficiency numbers that people paid so much for to get (the SEER) are no where near reached. Ive yet to see a service tech ever properly charge a system NEVER ever saw it done. If you want to find out exactly how to charge an AC and what pressures your system is required to have for a given temps and given RH. get a manual and read it as that is a very good way to learn about it so you would never be fooled. X Trane Engineer.3. Metal Halide vs High Pressure Sodium for plants?Be careful as these lamps generate a lot of heat. You will need some sort of ventilation to avoid overheating the plants. Keep in mind law enforcement agencies look for thermal signatures to find illegal pot production.4. Easy questions about weather?! Ten points!?Atmospheric pressure at the Earth's surface is one of the keys to weather, which is one reason weather maps feature H's and L's, representing areas of high and low air pressure. High and low pressure areas are important because they affect the weather. The weather maps, such as those on television, show what is happening at the Earth's surface, and that's what we are talking about here. As the name says, a "high" is an area where the air's pressure is higher than the pressure of the surrounding air. A "low' is where it's lower. Meteorologists do not have any particular number that divides high from low pressure; it's the relative differences that count. The pressure is high at the surface where air is slowly descending - much too slowly to feel. And, this is going on over a large area, maybe a few hundred square miles. As air descends, it warms, which inhibits the formation of clouds. This is why high pressure is generally - but not quite always - associated with good weather. The air that descends in high-pressure areas has to get to high altitudes in some way, and its done by rising in areas where the pressure at the surface is low. As air rises it cools. As the air cools, the humidity in it begins to condense into tiny drops of water, or if it's cold enough, into tiny ice crystals. If there's enough water or ice, rain or snow begin to fall. This is why low pressure is associated with bad weather. As shown in the graphic above, the air descending in high pressure flows out in a clockwise spiral in the Northern Hemisphere. Air flowing into an area of low pressure rises, making a counterclockwise spiral on the way in.
How to Understand the Equality About $(mathbfqcdot Mathrmgrad)mathbfq $?
How to Prove That $O(n) Cdot O(n^2) = O(n^3)$?
Show That $sup (Acdot B)=maxsup Acdotsup B, Sup Acdotinf B,inf Acdotsup B,inf Acdotinf B$
For How Many Integers $a$ Is $frac2^10 Cdot 3 ^8 Cdot 5^6a^4$ an Integer?
In Which Cases Does $(a Cdot B)^-1 = a^-1 Cdot B^-1$?
Droid Vs Blackberry Vs Iphone? HELP!?
Why Do Software Developers Tend to Leave a Company After 2 Or so Years?
Business Activities
Xiaomi Family Launched Intelligent Clothes Dryer
related searches
How to Understand the Equality About $(mathbfqcdot Mathrmgrad)mathbfq $?
For How Many Integers $a$ Is $frac2^10 Cdot 3 ^8 Cdot 5^6a^4$ an Integer?
In Which Cases Does $(a Cdot B)^-1 = a^-1 Cdot B^-1$?
How to Prove That $O(n) Cdot O(n^2) = O(n^3)$?
Show That $sup (Acdot B)=maxsup Acdotsup B, Sup Acdotinf B,inf Acdotsup B,inf Acdotinf B$
What Are Araya Rims Made of? Should I Replace Them?
Droid Vs Blackberry Vs Iphone? HELP!?
Why Do Software Developers Tend to Leave a Company After 2 Or so Years?
Business Activities

Copyright © 2020 Concises YuGa Sports | Sitemap