Each limit represents the derivative of some function f at some number a. Indicate an...

Redemitz4s

Redemitz4s

Answered

2021-11-24

Each limit represents the derivative of some function f at some number a. Indicate an f and a in each instance.
limt1t4t2t1

Answer & Explanation

Aretha Frazier

Aretha Frazier

Expert

2021-11-25Added 16 answers

Step 1
Consider the limit
limt1t4t2t1
We want to represent it as a derivative of some function f at some number a, ln light of definition 5 we want to write our limit in the form
limtaf(t)f(a)ta
Since t1 appears in the denominator, and t1, we are motivated to take a=1
Looking at the numerator of the limit in question we want f(t)=t4+t. Let us see if this is the right choice. By definition 5 we have
f(1)=limt1f(t)f(1)t1
=limt1t4+t(14+1)t1
=limt1t4+t2t1
Which is what we wanted to establish.
Ans: f(t)=t4+t, a=1
Hiroko Cabezas

Hiroko Cabezas

Expert

2021-11-26Added 18 answers

Step 1
Definition
f(a)=limxaf(x)f(a)xa
Step 2
limt1t4+t2t1
limt1(t4+t)(14+1)t1
limt1f(t)f(1)t1=f(1)
Where f(t)=t4+t
Note that a=1

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