# MAT284-2004Fall - MAT 284 1914541 Fall 2004(1 Find the...

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Unformatted text preview: MAT 284 1914541 Fall 2004 (1) Find the break even quantity q for product "Air; + 1600 ‘7 ifhonsumers will pay p : (100 ~ q) and when tlirr average cost is i; : (2) For f(I) 2- + (3)3 and g(:L') : 1 — \$2 find 9 o [(r). (3) Consumers will buy 30 units of a product if the price is \$10, and they will buy 40 units if the price is \$6. Assuming that the demand is linear ﬁnd the demand equation. \$5 (4) Write the expression In in terms of ln(z), ln(\$ + 1), ln(x + 2). x2 + 3 n 21:3 + 10 m _————_—_ 140° -—1:4 + 52:3 — 11 (5) Find the limits, justify your answers. lim - “ z—9-1‘ m +1 e (6) Use the deﬁnition to ﬁnd the derivative of f(z) = 6 — 2x + \$2. (7) Find the derivatives do not simplify. (a) <10z9 + 5—; + ln(:1:) + ex?) d2s-q3 dqq+3 (c) in + 3)(t2 +1)9 (8) For its best product a company knows that m workers will produce the quantityr q = 2m2+m per day. The demand function for the product is p = 2 . Find the marginal revenue q + ‘1 product when m = 10. (9) Elasticity of demand. The demand equation for a product is p = V5000 — qg. Find the elasticity of demand 7]. Describe the elasticity of demand when q : 50. (10) Find the intervals of increase, decrease, concave up, concave down, local extrema, and inﬂection points for y = 3x4 — 4x3. (11) The marginal cost for for a product is .4 q + 28 and the marginal revenue is 600 — 4q. Find the proﬁt maximizing output. (12) Find the antiderivatives do not simplifyi (a) /x3~8z2+%dz (b) /ez+§dm (c) /(\$2 + 3)4 xdx ...
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MAT284-2004Fall - MAT 284 1914541 Fall 2004(1 Find the...

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