Past 118 Final Problems

Past 118 Final Problems - Chap Problem Consider the...

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Chap Problem Source Seq 1 Consider the function () 2 6i f 5 8i f 5 tt ft tC t +< = −+ . a) Find the value of the constant C that makes the function ( ) f t continuous on , −∞ ∞ . b) Graph the function f t . c) Is the (resulting) continuous function ( ) f t differentiable at all points in the interval t −∞ < < ∞ ? Explain. 200105 1 1 Compute the following limits. If the limit is infinite, indicate whether it is +∞ or −∞ a) 2 21 lim 5 x x x →−∞ + + b) 2 12 lim 2 x x x + c) 2 2 1 1 lim 2 y y yy →− −− d) 2 2 lim 2 x x x x 200312 1 1 Let 2 2 1 1 1 1 11 1 1 1 x x x fx x x x x x −∞ < < − + + =− << + + a) List all the values of x for which f x is not continuous. Calculate the following limits. If the limit is infinite, indicate whether it is +∞ or −∞ . b) 1 lim x f x + c) 1 lim x f x d) 1 lim x f x + e) 1 lim x f x f) lim x f x →+∞ g) lim x f x →−∞ 200405 1
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Chap Problem Source Seq 1 Calculate the following limits. If the limit is infinite, indicate whether it is +∞ or −∞ . a) 4 4 lim 4 x x x + b) 2 4 16 lim 2 x x x c) 2 2 3 69 lim 9 t tt t →− ++ d) 2 2 lim 9 x xx x →∞ e) 0 42 lim t t t +− 200412 1 1 Consider the function () 3 41 2 2 3 fx x x +< = a) Find 3 f . b) Find 2 lim x f x c) Is f continuous at 2 x = ? Explain. d) Is f differentiable at 2 x = ? Explain 200512 2 2 Use the definition of the derivative to find the derivative of 2 1 3 x = . Then find an equation for the tangent line to the graph of f at 1 x = . 200105 2 2 Use the definition of the derivative to find ( ) f x where 2 1 x = + . 200112 1 2 a) Use implicit differentiation to find the slope of the tangent line to the curve 4 3 yx y + = at the point (4, 1). b) Find an equation of the tangent line to the curve 4 3 y + = at the point (4, 1). 200112 2 2 At a certain factory, the daily output is ( ) 600 QK K = units, where K denotes the capital investment measure in units of $1000. The current capital investment is $900,000. Use calculus to estimate the effect that an additional capital investment of $800 will have on the daily output. 200205 1 2 A manufacturer’s cost in dollars is 3 492 400 6 q Cq q =+ + , where q tons of steel are produced. The current level of production is 4 tons. Use calculus to estimate the amount by which the manufacturer should decrease production to reduce the cost by 100 dollars. 200305 1 2 Consider the curve defined by the equation 33 25 2 3 0 xy y x y +−+ = . Find the equation of the tangent line to the curve at the point ( ) ( ) ,1 , 2 xy = . 200305 2 2 In order to maintain the output of a certain factory at a constant level, the number x of permanent workers and the number y of temporary workers are related by the formula ( ) 2/3 1/2 80 10,400 y = Currently, the factory employs 1,000 permanent workers and 400 temporary workers.
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Past 118 Final Problems - Chap Problem Consider the...

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