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3 years ago

Pls help me my dads gonna hit me if i dont get this done

Mathematics

1 answer:

Tpy6a [65]3 years ago

3 0

Answer:

(I can't answer if its greater than, less than, or equal to because you didn't

specify the number I have to compare to)

2. $\frac{35}{8}$

3. greater than

4. $\frac{1}{9}$

5. $\frac{1}{6}$

6. $\frac{4}{5}$

Step-by-step explanation:

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Can you define f(0, 0) = c for some c that extends f(x, y) to be continuous at (0, 0)? If so, for what value of c? If not, expla

Ahat [919]

(i) Yes. Simplify $f(x,y)$ .

$\displaystyle \frac{x^2 - x^2y^2 + y^2}{x^2 + y^2} = 1 - \frac{x^2y^2}{x^2 + y^2}$

Now compute the limit by converting to polar coordinates.

$\displaystyle \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = \lim_{r\to0} \frac{r^4 \cos^2(\theta) \sin^2(\theta)}{r^2} = 0$

This tells us

$\displaystyle \lim_{(x,y)\to(0,0)} f(x,y) = 1$

so we can define $f(0,0)=1$ to make the function continuous at the origin.

Alternatively, we have

$\dfrac{x^2y^2}{x^2+y^2} \le \dfrac{x^4 + 2x^2y^2 + y^4}{x^2 + y^2} = \dfrac{(x^2+y^2)^2}{x^2+y^2} = x^2 + y^2$

and

$\dfrac{x^2y^2}{x^2+y^2} \ge 0 \ge -x^2 - y^2$

Now,

$\displaystyle \lim_{(x,y)\to(0,0)} -(x^2+y^2) = 0$

$\displaystyle \lim_{(x,y)\to(0,0)} (x^2+y^2) = 0$

so by the squeeze theorem,

$\displaystyle 0 \le \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} \le 0 \implies \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = 0$

and $f(x,y)$ approaches 1 as we approach the origin.

(ii) No. Expand the fraction.

$\displaystyle \frac{x^2 + y^3}{xy} = \frac xy + \frac{y^2}x$

$f(0,y)$ and $f(x,0)$ are undefined, so there is no way to make $f(x,y)$ continuous at (0, 0).

(iii) No. Similarly,

$\dfrac{x^2 + y}y = \dfrac{x^2}y + 1$

is undefined when $y=0$ .

5 0

1 year ago

3×3×5×5 as powers??

Feliz [49]

Answer:

= 225

Step-by-step explanation:

3 × 3 × 5 × 5

= 3² x 5²

= 9 x 25

= 225

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP.. WILL FAN AND MEDAL

Komok [63]

C. 18.88 centimeters. Because with a tilted radius of 5.7. It ranges up. So it would be a higher number SLIGHTLY.
Hope this helps.

4 0

3 years ago

Read 2 more answers

Drag and drop the correct surface area to match the cube. cube with edge length = 3.2 m 12.8 m²19.2 m²51.2 m²61.44 m²

Ira Lisetskai [31]

- Surface Area of a Cube = 6(L)²
- Surface Area of this cube = 6(3.2)²
= 61.44 m²

3 0

3 years ago

Describe a sequence of transformations that can be performed to polygon ABCDE to prove that it is similar to polygon FGHIJ

maxonik [38]

Answer:

answer below

Step-by-step explanation:

ABCDE go through dilation over center (6 , -2) with factor of 1/2 to FGHIJ

AB // FG slope: -2 , √20:√5 = 2: 1

BC // GH // X axis 8:4 = 2:1

CD // HI, slope= 1 , √8:√2 = 2:1

DE // IJ // x axis, 4:2 = 2:1

EA // JF // y axis, 2:1

8 0

2 years ago