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### 17 Cards in this Set

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 lim(x→a) [f(x) + g(x)] = lim(x→a)f(x) + lim(x→a)g(x) lim(x→a) [c f(x)] = c lim(x→a) f(x) lim(x→a) [f(x) ÷ g(x)] = lim(x→a)f(x) ÷ lim(x→a)g(x) if lim(x→a)g(x) ≠ 0 lim(x→a) [f(x)]n = [ lim(x→a) f(x) ]^n where n is a positive integer The Squeeze Theorem If f(x) ≤ g(x) ≤ h(x) when x is near a (except possibly at a) and lim(x→a) f(x) = lim(x→a) h(x) = L then lim(x→a) h(x) = L (derivative of a constant function) d/dx (c) = 0 d/dx (x) = 1 (power rule) d/dx (x^n) = nx^(n-1) (the constant multiple rule) d/dx [cf(x)] = c d/dx f(x) (the sum rule) d/dx [f(x) + g(x)] = d/dx f(x) + d/dx g(x) (the difference rule) d/dx [f(x) - g(x)] = d/dx f(x) - d/dx g(x) (the product rule) d/dx [f(x)g(x)] = f(x) d/dx[ g(x)] + g(x) d/dx[ f(x)] (the quotient rule) d/dx [f(x) / g(x)] = ( g(x) d/dx[f(x)] - f(x) d/dx[g(x)] ) ÷ [g(x)]^2 (the chain rule) F'(x) = f '(g(x)) • g'(x) Leibniz notiation: dy/dx = (dy/du) (du/dx) (the chain rule & power rule) d/dx [g(x)]^n = n[g(x)]^(n-1) • g'(x) Alternatively: d/dx [u^n] = nu^(n-1) du/dx Formal Definition of a Derivative The tangent line to the curve y=f(x) at the pointP(a, f(a)) is the line through P with the slope... m = lim(x→a) [(f(x) - f(a)] / [x - a] Formal Definition of a Derivative Using H The tangent line to the curve y=f(x) at the pointP(a, f(a)) with (h = x - a) & (x = a + h) is the line through P with the slope... m = lim(h→0) [(f(a+h) - f(a)] / h