A system of equations is shown below
1 answer:
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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
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.
Answer:
Step-by-step explanation:
To find the function, compare the y values. Notice that each y value decreases by being divided by 4. This means the base of the exponential is 1/4.
To find the initial value, consider the point (0,0.5). When 1/4 is raised to the 0 power, the value is 1. This leaves that the initial value is 1/2 since 1/2*1 = 0.5.
The function is .