According to the definition of a function, since every element in the domain should be mapped to a single element in the codomain, the output of -2 should be either 2 or -1 but not both.
Note that the other elements in the domain have unique images.
So, to make the mapping a function, we need to remove (-2, 2) or (-2, -1).
Of these, (-2, -1) is only given in the options.
Hence, the ordered pair to be removed is (-2, -1).
The 2 is 100th place the 0 is 10th place the 9 is ones place the 4 is 1,000 place and the 5 is 10,000 place
The answer to the question is A
Answer:
![y=exp(\int\limits^x_4 {e^{-t^{2} } } \, dt)](https://tex.z-dn.net/?f=y%3Dexp%28%5Cint%5Climits%5Ex_4%20%7Be%5E%7B-t%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dt%29)
Step-by-step explanation:
This is a separable equation with an initial value i.e. y(3)=1.
Take y from right hand side and divide to left hand side ;Take dx from left hand side and multiply to right hand side:
![\frac{dy}{y} =e^{-x^{2} }dx](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7By%7D%20%3De%5E%7B-x%5E%7B2%7D%20%7Ddx)
Take t as a dummy variable, integrate both sides with respect to "t" and substituting x=t (e.g. dx=dt):
![\int\limits^x_3 {\frac{1}{y} } \, \frac{dy}{dt} dt=\int\limits^x_3 {e^{-t^{2} } } dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ex_3%20%7B%5Cfrac%7B1%7D%7By%7D%20%7D%20%5C%2C%20%5Cfrac%7Bdy%7D%7Bdt%7D%20dt%3D%5Cint%5Climits%5Ex_3%20%7Be%5E%7B-t%5E%7B2%7D%20%7D%20%7D%20dt)
Integrate on both sides:
![ln(y(t))\left \{ {{t=x} \atop {t=3}} \right. =\int\limits^x_3 {e^{-t^{2} } } \, dt](https://tex.z-dn.net/?f=ln%28y%28t%29%29%5Cleft%20%5C%7B%20%7B%7Bt%3Dx%7D%20%5Catop%20%7Bt%3D3%7D%7D%20%5Cright.%20%3D%5Cint%5Climits%5Ex_3%20%7Be%5E%7B-t%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dt)
Use initial condition i.e. y(3) = 1:
![ln(y(x))-(ln1)=\int\limits^x_3 {e^{-t^{2} } } \, dt\\ln(y(x))=\int\limits^x_3 {e^{-t^{2} } } \, dt\\](https://tex.z-dn.net/?f=ln%28y%28x%29%29-%28ln1%29%3D%5Cint%5Climits%5Ex_3%20%7Be%5E%7B-t%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dt%5C%5Cln%28y%28x%29%29%3D%5Cint%5Climits%5Ex_3%20%7Be%5E%7B-t%5E%7B2%7D%20%7D%20%7D%20%5C%2C%20dt%5C%5C)
Taking exponents on both sides to remove "ln":
Answer:
233600
Step-by-step explanation:
46x600=27600
27600
100x1000=1000000
=233600
Have a nice day