As these questions are coming straight off my chapter review assignment and my test is coming up next week, any help with the concepts, procedures, and answers to any or (if you're feeling long winded!) all of these problems would be greatly appreciated. I understand the basics, but these are the ones that left me stumped.
1. An equation for a tangent line to the graph of y=arctan(x/3) at the origin is:
2. A solution to the equation dx/dy+2xy=0 that contains the point (0,e) is
a) y= e^(1-x^2)
b) y=e^(1+x^2)
c) y=e^(1-x)
d) y=e^(1+x)
c) y=e^(x^2)
3. If g1(x)=2g(x) and g(-1)=1, then g(x) is:
a) e^(2x)
b) e^(-x)
c) e^(x+1)
d) e^(2x+2)
e) e^(2x-2) note:
"g1(x)" is meant to be read as "g prime of x"
4. Show that if C is a constant, y=x-1+Ce^(-x) is a solution to the differential equation (dy/dx)=x-y
5. The point (1,9) lies on the graph of an equation y=f(x) for which (dy/dx)=y^(1/2)4x where x is greater than or equal to 0 and y is greater than or equal to 0. When x=0 the value of y is a) 6
b) 4
c) 2
d) 2^(1/2) or the square root of 2
e) 0
Thank you! I realize 5 is a lot of problems to post, but the assignment was huge and I am having even huger troubles trying to figure this stuff out.
1. An equation for a tangent line to the graph of y=arctan(x/3) at the origin is:
2. A solution to the equation dx/dy+2xy=0 that contains the point (0,e) is
a) y= e^(1-x^2)
b) y=e^(1+x^2)
c) y=e^(1-x)
d) y=e^(1+x)
c) y=e^(x^2)
3. If g1(x)=2g(x) and g(-1)=1, then g(x) is:
a) e^(2x)
b) e^(-x)
c) e^(x+1)
d) e^(2x+2)
e) e^(2x-2) note:
"g1(x)" is meant to be read as "g prime of x"
4. Show that if C is a constant, y=x-1+Ce^(-x) is a solution to the differential equation (dy/dx)=x-y
5. The point (1,9) lies on the graph of an equation y=f(x) for which (dy/dx)=y^(1/2)4x where x is greater than or equal to 0 and y is greater than or equal to 0. When x=0 the value of y is a) 6
b) 4
c) 2
d) 2^(1/2) or the square root of 2
e) 0
Thank you! I realize 5 is a lot of problems to post, but the assignment was huge and I am having even huger troubles trying to figure this stuff out.