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rewona [7]
2 years ago
10

the cooper family decided to hike to hillside lake,approximately 8⅝ miles away. after an hour tje lake was still 5⅓ miles away.

hpw far did the group so far?​
Mathematics
2 answers:
alisha [4.7K]2 years ago
7 0

Answer: 3 7/24

Step-by-step explanation:

Given: The Cooper family decided to hike to Hillside Lake.

The approximate distance to travel for Hillside Lake = 8 5/8

Since , After an hour the lake was still away. 5 1/3

Now, the distance hiked by group :

8 5/8 - 5 1/3 = 3 7/24

ollegr [7]2 years ago
7 0

Answer= 3\7-24 miles

Step-by-step explanation:

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  • To show exixtance of f_x(0,0), f_y(0,0) we take,

f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

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f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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2 years ago
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