Consider the function defined by F(x, y) = xy(2x^2 + 6y^2)/x^2 + y^2
except at (x, y) = (0, 0) where F(0, 0) = 0. Then we have
partial differential/partial differential y partial differential F/partial differential z (0, 0) =
partial differential/partial differential z partial differential F/partial differential y (0, 0) =
Note that the answers are different. The existence and continuity of all second partials in a region around a point guarantees the equality of the two mixed second derivatives at the point. In the above case, continuity fails at (0,0).

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

the answer to 1/4x+5/3x-4=2-1/12x is x=3

hope this if needed hmu