(a) what is wrong with the following equation? x2 + x − 2 x − 1 = x + 2 (x − 1)(x + 2) ≠ x2 + x − 2 the left-hand side is not defined for x = 0, but the right-hand side is. the left-hand side is not defined for x = 1, but the right-hand side is. none of these — the equation is correct. (b) in view of part (a), explain why the equation lim x → 1 x2 + x − 2 x − 1 = lim x → 1 (x + 2) is correct. since x2 + x − 2 x − 1 and x + 2 are both continuous, the equation follows. since the equation holds for all x ≠ 1, it follows that both sides of the equation approach the same limit as x → 1. this equation follows from the fact that the equation in part (a) is correct. none of these — the equation is not correct.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

the monthly balance will be $75,000

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.