Αποτελέσματα Αναζήτησης
Integration Formulas Z dx = x+C (1) Z xn dx = xn+1 n+1 +C (2) Z dx x = ln|x|+C (3) Z ex dx = ex +C (4) Z ax dx = 1 lna ax +C (5) Z lnxdx = xlnx−x+C (6) Z sinxdx = −cosx+C (7) Z cosxdx = sinx+C (8) Z tanxdx = −ln|cosx|+C (9) Z cotxdx = ln|sinx|+C (10) Z secxdx = ln|secx+tanx|+C (11) Z cscxdx = −ln |x+cot +C (12) Z
1. Limits. Properties. if lim f ( x ) = l and lim g ( x ) = m , then. x → a x → a. lim [ f ( x ) ± g ( x ) ] = l ± m. x → a. lim [ f ( x ) ⋅ g ( x ) ] = l ⋅ m. → a. ( x ) l. lim = x → a. g ( x ) m. where m ≠ 0. lim c ⋅ f ( x ) = c ⋅ l. → a. 1. lim = where l ≠ 0. x → a f ( x ) l. Formulas. . n 1 lim 1 + = e. →∞ . . lim ( 1 + n )1. n = e.
In the table below, ? œ 0ÐBÑ and @ œ 1ÐBÑ represent differentiable functions of B. ) -? ( . œ ! . B .- œ - .? Ð We could also write Ð-0Ñ w œ -0 w , and could use the “prime notion” in the other formulas as well) . ( ? „ @ ) œ „ .? .@ . B .B .B.
Differentiation Formulas. Derivatives of Basic Functions. Derivatives of Logarithmic and Exponential Functions. Derivatives of Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Differentiation Rules.
Formulas: (note: u is a function of x) (sin(x)) = cos(x) dx. (2) (cos(x)) = sin(x) dx. d. (3) (tan(x)) = sec2(x) dx. d. (4) (sec(x)) = sec(x) tan(x) dx. d. (5) (cot(x)) = dx.
Diferentiation Formulas. General Formulas. : . c = . d −. 2. Power Rule: 1 , x dx. n. . d. 3. Scalar Multiple of a Function: c f ( dx. dx. 5. Product Rule: f ( x ) g ( f ( x ) g ( x ) + g ( x ) f ( x ) dx x ) = g. 6. Quotient Rule: ( ) = 2. g. d. 7. Chain Rule: f ( g ( x ) ) = f g ( x ) g ( x ) dx.
Basic Differentiation Rules Basic Integration Formulas DERIVATIVES AND INTEGRALS © Houghton Mifflin Company, Inc. 1. 4. 7. 10. 13. 16. 19. 22. 25. 28. 31. 34.
