1. Evaluate the following limits using algebraic methods. If the limit does not exist, explain why, using the definition
Posted: Tue Jul 12, 2022 12:53 pm
1. Evaluate the following limits using algebraic methods. If thelimit does not exist, explain why, using the definition of thelimit.
lim π₯3β1/π₯3+5 when π₯ββ lim 5π₯3β8/4π₯2+5π₯ whenπ₯ββ
2.Determine: (a) the derivative of each function using the limitdefinition of the derivative; (b) the instantaneous rate of changeof the function at the given value; (c) the tangent line that goesthrough the given x-value.
a. π(π₯)=5π₯2 +6π₯β11;π₯=β2
b. π(π)=2π2β4π+5;π=2
3. Suppose the productivity of a worker (in units per hour)after x hours of training and time on the
70π₯2 job is given by: π(π₯) = 3 + π₯2+1000.
Find and interpret π(20).
Find and interpret πβ²(20).
4.
π₯2
14) A small business has weekly costs of πΆ(π₯) = 100 + 30π₯ + 10,where x is the number of units
produced each week. The competitive market price for thisbusinessβ product is $46 per unit. Find the marginal profit.
lim π₯3β1/π₯3+5 when π₯ββ lim 5π₯3β8/4π₯2+5π₯ whenπ₯ββ
2.Determine: (a) the derivative of each function using the limitdefinition of the derivative; (b) the instantaneous rate of changeof the function at the given value; (c) the tangent line that goesthrough the given x-value.
a. π(π₯)=5π₯2 +6π₯β11;π₯=β2
b. π(π)=2π2β4π+5;π=2
3. Suppose the productivity of a worker (in units per hour)after x hours of training and time on the
70π₯2 job is given by: π(π₯) = 3 + π₯2+1000.
Find and interpret π(20).
Find and interpret πβ²(20).
4.
π₯2
14) A small business has weekly costs of πΆ(π₯) = 100 + 30π₯ + 10,where x is the number of units
produced each week. The competitive market price for thisbusinessβ product is $46 per unit. Find the marginal profit.