Calculus 1: Test 1
Intermediate Value Theorem - correct answer-Suppose f(x) is continuous on a closed
interval [a,b] and f(a) ≠ f(b). For every number N between f(a) and f(b), there is a value c ∈
[a,b] such that f(c) = N.
The Chain Rule Combined with the Power Rule - correct answer-If n is any real number and
u = g(x) is differentiable, then (uⁿ)'= nuⁿ⁻¹ × u'.
Or [g(x)]ⁿ' = n[g(x)]ⁿ⁻¹ × g'(x)
The Squeeze Theorem - correct answer-Let f(x) < g(x) < h(x) for all x ∈ I except possibly at
x = a ∈ I.
If lim (x→a) f(x) = lim (x→a) h(x) = L, then lim (x→a) g(x) = L.
Intermediate Value Theorem - correct answer-Suppose f(x) is continuous on a closed
interval [a,b] and f(a) ≠ f(b). For every number N between f(a) and f(b), there is a value c ∈
[a,b] such that f(c) = N.
The Chain Rule Combined with the Power Rule - correct answer-If n is any real number and
u = g(x) is differentiable, then (uⁿ)'= nuⁿ⁻¹ × u'.
Or [g(x)]ⁿ' = n[g(x)]ⁿ⁻¹ × g'(x)
The Squeeze Theorem - correct answer-Let f(x) < g(x) < h(x) for all x ∈ I except possibly at
x = a ∈ I.
If lim (x→a) f(x) = lim (x→a) h(x) = L, then lim (x→a) g(x) = L.
