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AlsoI need a need step by step process how how you arrived at the answer and explanations ( espically for the graphs).
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MAC 2233 Test Chapters 1 and 2 Name___________________________________ A. Goldstein 5 points each Decide whether the limit exists. If it exists, find its value. 1) Find 1) a. lim f(x) b. lim f(x) c. lim f(x) - + x 0 x 0 x 0 Find the limit, if it exists. 2 x - 9 2) lim 2) x- 3 x 3 3) Find the limit, if it exists. 3) x- 4 lim x- 2 x 4 12 x + 4, for x<>
MAC 2233 Test Chapters 1 and 2 Name___________________________________ A. Goldstein 5 points each Decide whether the limit exists. If it exists, find its value. 1) Find a. lim x 0- f(x) b. lim x 0+ f(x) c. lim x 0 f(x) 1) Find the limit, if it exists. 2) lim x 3 x2 - 9 x - 3 2) 3) Find the limit, if it exists. lim x 4 x - 4 x - 2 3) 1 4) Is the function given by f(x) = x2 + 4, for x < 0 2, for x 0 continuous at x =0? why or why not? 4) write the definition of the deriviative f'(x) using limits. find the derivative of the function using the definition 5) f(x) = 6x2 5) find an equation for the line tangent to the graph of the given function at the indicated point. 6) f(x) = x 3 2 at (-6, - 108) 6) 2 differentiate 7) f(x) = 9x7/5 - 5x2 + 10x4 7) evaluate the derivative at the given value of x. 8) if y = 7 x - x, find dy dx x = 4 8) find all values of x (if any) where the tangent line to the graph of the function is horizontal. 9) y = x3 - 12x + 2 9) 3 solve the problem. 10) if the price (in dollars) of a product is given by p(x) = 1024 x + 1100, where x represents the demand for the product, find the rate of change of price when the demand is 32 units. 10) numbers 11- 18: differentiate: 11) y = (x2 + 2)3 11) 12) y = x 3 x - 1 12) 4 13) h(r) = r 2 - 4r + 8 3r + 2 13) differentiate. 14) f(x) = (4x2 - 3)10 14) 15) f(x) = 1 2x2 + 7 15) 5 16) f(x) = 1 (4x2 - 9x + 5)4 16) 17) f(x) = 4x + 4 x - 2 5 17) 18) y = x x2 + 1 18) 6 solve the problem. 19) if s is a distance given by s t = 4t4 + 4t3 + 4t , find the velocity, v(t) and the acceleration, a(t). 19) 20) the revenue, in dollars, from the sale of x compact disc players is r(x) = x3 - 4x2 + 4x + 6. a. find the marginal revenue. b. find the marginal revenue to estimate the revenue derived from the sale of the fourth unit. 20) 7 0="" 2,="" for="" x="" 0="" continuous="" at="" x="0?" why="" or="" why="" not?="" 4)="" write="" the="" definition="" of="" the="" deriviative="" f'(x)="" using="" limits.="" find="" the="" derivative="" of="" the="" function="" using="" the="" definition="" 5)="" f(x)="6x2" 5)="" find="" an="" equation="" for="" the="" line="" tangent="" to="" the="" graph="" of="" the="" given="" function="" at="" the="" indicated="" point.="" 6)="" f(x)="x" 3="" 2="" at="" (-6,="" -="" 108)="" 6)="" 2="" differentiate="" 7)="" f(x)="9x7/5" -="" 5x2="" +="" 10x4="" 7)="" evaluate="" the="" derivative="" at="" the="" given="" value="" of="" x.="" 8)="" if="" y="7" x="" -="" x,="" find="" dy="" dx="" x="4" 8)="" find="" all="" values="" of="" x="" (if="" any)="" where="" the="" tangent="" line="" to="" the="" graph="" of="" the="" function="" is="" horizontal.="" 9)="" y="x3" -="" 12x="" +="" 2="" 9)="" 3="" solve="" the="" problem.="" 10)="" if="" the="" price="" (in="" dollars)="" of="" a="" product="" is="" given="" by="" p(x)="1024" x="" +="" 1100,="" where="" x="" represents="" the="" demand="" for="" the="" product,="" find="" the="" rate="" of="" change="" of="" price="" when="" the="" demand="" is="" 32="" units.="" 10)="" numbers="" 11-="" 18:="" differentiate:="" 11)="" y="(x2" +="" 2)3="" 11)="" 12)="" y="x" 3="" x="" -="" 1="" 12)="" 4="" 13)="" h(r)="r" 2="" -="" 4r="" +="" 8="" 3r="" +="" 2="" 13)="" differentiate.="" 14)="" f(x)="(4x2" -="" 3)10="" 14)="" 15)="" f(x)="1" 2x2="" +="" 7="" 15)="" 5="" 16)="" f(x)="1" (4x2="" -="" 9x="" +="" 5)4="" 16)="" 17)="" f(x)="4x" +="" 4="" x="" -="" 2="" 5="" 17)="" 18)="" y="x" x2="" +="" 1="" 18)="" 6="" solve="" the="" problem.="" 19)="" if="" s="" is="" a="" distance="" given="" by="" s="" t="4t4" +="" 4t3="" +="" 4t="" ,="" find="" the="" velocity,="" v(t)="" and="" the="" acceleration,="" a(t).="" 19)="" 20)="" the="" revenue,="" in="" dollars,="" from="" the="" sale="" of="" x="" compact="" disc="" players="" is="" r(x)="x3" -="" 4x2="" +="" 4x="" +="" 6.="" a.="" find="" the="" marginal="" revenue.="" b.="" find="" the="" marginal="" revenue="" to="" estimate="" the="" revenue="" derived="" from="" the="" sale="" of="" the="" fourth="" unit.="" 20)="">