# Calculus Stuff

63 cards

Calculus. That's all you need to know.

Created Oct 16, 2011
by
pikabolt

 Shuffle Cards

# Flashcard Set Preview

 Side A Side B 1 Derivative of a Constant d/dx (c) = 0 2 Power Rule d/dx (xn) = nxn-1 3 Constant Multiple Rule d/dx [cf(x)] = cf'(x) 4 Sum Rule d/dx [f(x) + g(x)] = f'(x) + g'(x) 5 Difference Rule d/dx [f(x) - g(x)] = f'(x) - g'(x) 6 Product Rule d/dx [f(x) g(x)] = f'(x) g(x) + g'(x) f(x) 7 Quotient Rule d/dx [f(x)/g(x)] = [f'(x) g(x) - g'(x) f(x)]/[g(x)]2 8 Derivative of Sine d/dx (sin x) = cos x 9 Derivative of Cosine d/dx (cos x) = -sin x 10 Derivative of Tangent d/dx (tan x) = sec2 x 11 Derivative of Cosecant d/dx (csc x) = -csc x cot x 12 Derivative of Secant d/dx (sec x) = sec x tan x 13 Derivative of Cotangent d/dx (cot x) = -csc2 x 14 Chain Rule d/dx {f[g(x)]} = f'[g(x)] g'(x) 15 Power Chain Rule d/dx {[f(x)]n} = n[f(x)]n-1 f'(x) 16 Differential dy = f'(x) dx 17 Inverse Function Theorem d/dx [f-1(x)] = 1/f'[f-1(x)] 18 Exponential Addition nx+y = nx ny 19 Exponential Subtraction nx-y = nx/ny 20 Exponential Multiplication nxy = (nx)y 21 Combinational Exponents (cn)x = cx nx 22 Derivative of Natural Exponential Function d/dx (enx) = nenx 23 Derivative of Logarithmic Functions d/dx [ln f(x)] = f'(x)/f(x) 24 Linearization Formula L(x) = f(a) + f'(a) (x - a) 25 Differentials dy = f'(x) dx 26 Absolute Maximum f(c) ≥ f(x) for all x in D 27 Absolute Minimum f(c) ≤ f(x) for all x in D 28 Local Maximum f(c) ≥ f(x) when x is near c 29 Local Minimum f(c) ≤ f(x) when x is near c 30 Mean Value Theorem f'(c) = [f(b) - f(a)]/(a - b) 31 Increasing Function f'(x) > 0 32 Decreasing Function f'(x) < 0 33 Concave Up f"(x) > 0 34 Concave Down f"(x) < 0 35 Local Minimum II f'(x) = 0 and f"(x) > 0 36 Local Maximum II f'(x) = 0 and f"(x) < 0 37 Horizontal Asymptotes f(x) => H as x => ∞ or -∞ 38 Vertical Asymptotes f(x) => ∞ or -∞ as x => V 39 Even Function f(-x) = f(x) for all x in D 40 Odd Function f(-x) = f(-x) for all x in D 41 Periodic Function f(x + p) = f(x) for all x in D 42 Newton's Method xn+1  = xn - f(xn)/f'(xn) 43 Moving Upwards f(x) + c 44 Moving Downwards f(x) - c 45 Moving RIghtwards f(x - c) 46 Moving Leftwards f(x + c) 47 Vertical Stretching cf(x) 48 Vertical Shrinking f(x)/c 49 Horizontal Shrinking f(cx) 50 Horizontal Stretching f(x/c) 51 Vertical Reflecting -f(x) 52 Horizontal Reflecting f(-x) 53 Limit Law #1 lim [f(x) + g(x)] = lim f(x) + lim g(x) 54 Limit Law #2 lim [f(x) - g(x)] = lim f(x) - lim g(x) 55 Limit Law #3 lim [cf(x)] = c lim f(x) 56 Limit Law #4 lim [f(x) g(x)] = lim f(x) lim g(x) 57 Limit Law #5 lim [f(x)/g(x)] = lim f(x)/lim g(x) 58 Limit Law #6 lim [f(x)n] = [lim f(x)]n 59 Limit Law #7 lim c = c 60 Limit Law #8 lim x = a 61 Limit Law #9 lim xn = an 62 LImit Law #10 lim x1/n = a1/n 63 Limit Law #11 lim [f(x)1/n] = [lim f(x)]1/n

No comments yet! Be the first to add a comment below!