You're trying 5 sample problems.

Join to unlock the full course.

Problem

Calculus I

A Difference Quotient Settles Down

Let $s(t)=4t-t^2$ . For $h\neq 0$ , the average rate of change of $s$ on the interval with endpoints $3$ and $3+h$ is $\frac{s(3+h)-s(3)}{h}.$ Evaluate $\lim_{h\to 0}\frac{s(3+h)-s(3)}{h}.$ Show the algebraic simplification that is valid for $h\neq 0$ , and explain why that simplification determines the limit even though the original difference quotient is undefined at $h=0$ .

Definition

Definition for this problem

Show commentary

Hints are here to help; nothing is recorded.

Your answer

Limit

Type / for a fraction, ^ for a power, sqrt for a root, pi for π.

TrainCoursesProblemsProgressMoreTrain Courses Problems Progress

More

Proof Blocks Tools Account

ProofAnvil Practice$19 USD monthly · cancel any time

Pricing FAQ Features Roadmap Use with your agent Support Terms Privacy Refunds

Training · ProofAnvil