The slope field for a certain differential equation is shown above. Which of the following could be the particular solution to the differential equation satisfying y(0)=0
?

Responses
A) y = −cosx + 1
B) y = e^x^2 − 1
C) y = sinx
D) y = tanx

The Slope Field For A Certain Differential Equation Is Shown Above. Which Of The Following Could Be The

Answers

Answer 1

y = −cosx + 1, This function does not equal zero at x = 0 and has a horizontal asymptote of y = 1. Thus, the solution fulfilling y(0) = 0 cannot be that specific solution.

If the degree of the numerator is, then a rational function will have a horizontal asymptote of y = 0.

When the degree of the polynomial in the numerator is lower than the degree of the polynomial in the denominator, a rational function has the horizontal asymptote y=0. In these situations, the horizontal asymptote lies on the x-axis.

What is the asymptotic rule for horizontal lines?

By examining the degrees of the numerator (n) and denominator, we can locate the horizontal asymptote (m). Y=an / bm is the horizontal asymptote if n n=m.

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