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Vlada [557]
3 years ago
12

Similarly, approaching along the y-axis yields a limit equal to 0. Since these two limits are the same, we will examine another

approach path. Approach (0, 0) along the curve y = x2. When x is positive, we have lim (x, y) → (0, 0) xy x2 + y2 =
Mathematics
1 answer:
djverab [1.8K]3 years ago
3 0

Answer:

This approach to (0,0) also gives the value 0

Step-by-step explanation:

Probably, you are trying to decide whether this limit exists or not. If you approach through the parabola y=x², you get

\lim_{(x,y)\rightarrow (0,0)}\frac{xy}{\sqrt{x^2+y^2}}=\lim_{(x,x^2)\rightarrow (0,0)}\frac{xx^2}{\sqrt{x^2+(x^2)^2}}=\lim_{x\rightarrow 0}\frac{x^3}{|x|\sqrt{1+x^2}}=0

It does not matter if x>0 or x<0, the |x| on the denominator will cancel out with an x on the numerator, and you will get the term x²/(√(1+x²) which tends to 0.

If you want to prove that the limit doesn't exist, you have to approach through another curve and get a value different from zero.

However, in this case, the limit exists and its equal to zero. One way of doing this is to change to polar coordinates and doing a calculation similar to this one. Polar coordinates x=rcosФ, y=rsinФ work because the limit will only depend on r, no matter the approach curve.

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12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5
Murljashka [212]

Answer:

\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}

Step-by-step explanation:

\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/

\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}

\text{Despite this, let's check the ratios}

\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5

\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}

8 0
3 years ago
The distance d, in meters, that a rhinoceros runs in s seconds is represented by the equation d=16s. What is the constant of pro
castortr0y [4]
Time          Distance                Distance / Time
2hrs          90 miles                  90 miles / 2 hrs =  45 miles / hr
3hrs          135 miles                135 miles / 3 hrs =  45 miles / hr
5hrs          225 miles                 225 miles / 5 hrs =  45 miles / hr
6hrs          270 miles                  270 miles / 6 hrs =  45 miles / hr

Constant of proportionality is 45 miles / hr. This is the same for the four values. The unit rate is also 45 miles / hr.

Let us assume the Distance , d is directly proportional to Time, t
d α t
d = kt 
Constant of proportionality is k which is D/T
d = 45t 

3 0
3 years ago
How long does it take a truck traveling at a velocity of 90 km/hr to travel 990 km.?
makvit [3.9K]

Answer:

10 hr

Step-by-step explanation:

i divided 990 by 90 and got 10 hr

3 0
2 years ago
Read 2 more answers
A file that is 228 megabytes is being downloaded. If the download is 12.4% complete, how many megabytes have been downloaded? Ro
Otrada [13]
228-12.4%= 199.728
199.728 rounded to the nearest tenth is *199.7*
3 0
3 years ago
A rectangular garden has a total area of 48 square yards.Draw and label2 possiblerectangular garden with different side lengths
erastovalidia [21]

Answer:

see diagram

Step-by-step explanation:

A rectangle has the area that can be calculated using formula

A=\text{length}\cdot \text{width}.

1. Consider rectangle with length of 8 yards and width of 6 yard. Then

A=6\cdot 8=48\ yd^2.

2. Consider rectangle with length of 12 yards and width of 4 yard. Then

A=12\cdot 4=48\ yd^2.

These two rectangles are attached.

4 0
3 years ago
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