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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.1 The Derivative of a Function, #1 · Calculus · Derivatives

(d)

Which of the following numbers (as is) gives $df / d t$ at time $t$ ?
If in doubt test on $f (t) = t^{2}$ .

(a) $\frac{f ( t + Δ t ) - f ( t )}{Δ t}$

(b) $lim_{h \to 0} \frac{f ( t + 2 h ) - f ( t )}{2 h}$

(c) $lim_{Δ t \to 0} \frac{f ( t - Δ t ) - f ( t )}{- Δ t}$

(d) $lim_{t \to 0} \frac{f ( t + Δ t ) - f ( t )}{Δ t}$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.1 The Derivative of a Function, #1

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