Use suitable linear approximation to find the approximate values for given functions at the points indicated:

$f(x,y)=x{e}^{y+{x}^{2}}$

$f(x,y)=x{e}^{y+{x}^{2}}$

veleumnihryz
2022-05-03
Answered

Use suitable linear approximation to find the approximate values for given functions at the points indicated:

$f(x,y)=x{e}^{y+{x}^{2}}$

$f(x,y)=x{e}^{y+{x}^{2}}$

You can still ask an expert for help

bailaretzy33

Answered 2022-05-04
Author has **15** answers

Let $L(x,y)$=$f({x}_{0},{y}_{0})+{f}_{x}({x}_{0},{y}_{0})(x-{x}_{0})+{f}_{y}({x}_{0},{y}_{0})(y-{y}_{0})$. Then $L(x,y)\approx f(x,y)$. Consider $({x}_{0},{y}_{0})=(2,-4)$. Then,

$L(x,y)=2+9(x-2)+2(y+4)\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}f(2.05,-3.92)\approx L(2.05,-3.92)=2.61$

Notice, from a calculator, $f(2.05,-3.92)=2.7192$

$L(x,y)=2+9(x-2)+2(y+4)\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}f(2.05,-3.92)\approx L(2.05,-3.92)=2.61$

Notice, from a calculator, $f(2.05,-3.92)=2.7192$

Diya Bass

Answered 2022-05-05
Author has **20** answers

Denoting the partial derivatives by ${f}_{x}^{\prime}$ and ${f}_{y}^{\prime}$, the formula is:

$f({x}_{0}+h,{y}_{0}+k)=f({x}_{0},{y}_{0})+{f}_{x}^{\prime}({x}_{0},{y}_{0})h+{f}_{y}^{\prime}({x}_{0},{y}_{0})k+o{\textstyle (}\Vert (h,k)\Vert {\textstyle )}.$

$f({x}_{0}+h,{y}_{0}+k)=f({x}_{0},{y}_{0})+{f}_{x}^{\prime}({x}_{0},{y}_{0})h+{f}_{y}^{\prime}({x}_{0},{y}_{0})k+o{\textstyle (}\Vert (h,k)\Vert {\textstyle )}.$

asked 2022-05-10

Use the linear approximation of Use the linear approximation of f(x,y)=e2x2+3y at (0,0) to estimate f(0.01,−0.02). at $(0,0)$ to estimate $f(0.01,-0.02)$.

asked 2022-05-10

Linear approximation to find $\frac{1}{4.002}$

asked 2022-05-10

Determine how accurate should we measure the side of a cube so that the calculated surface area of the cube lies within $3$% of its true value, using Linear Approximation.

Let $A(x)=TSA$; $x=side$

$A(x)=6{x}^{2}$

Let $A(x)=TSA$; $x=side$

$A(x)=6{x}^{2}$

asked 2022-05-10

Find the linear approximation $Y$ to $f(x)$ near $x=a$.

$f(x)=x+{x}^{4},\phantom{\rule{1em}{0ex}}a=0$

$f(x)=x+{x}^{4},\phantom{\rule{1em}{0ex}}a=0$

asked 2022-05-09

Use linear approximation, i.e. the tangent line, to approximate ${11.2}^{2}$ as follows :

Let $f(x)={x}^{2}$ and find the equation of the tangent line to $f(x)$ at $x=11$. Using this, find your approximation for ${11.2}^{2}$.

Let $f(x)={x}^{2}$ and find the equation of the tangent line to $f(x)$ at $x=11$. Using this, find your approximation for ${11.2}^{2}$.

asked 2022-05-08

Let $l(x)$ be the linear approximation of $f(x)={x}^{2/5}$ at $a=32$. Approximation?

asked 2022-04-07

Use linear approximation to estimate $\mathrm{tan}(\frac{\pi}{4}+0.05)$. Identify the differentials $dy$ and $d$ in the situation.