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# Calculus 1, Week 5 Notes 21-111

CMU

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This 2 page Class Notes was uploaded by Monica Chang on Saturday October 1, 2016. The Class Notes belongs to 21-111 at Carnegie Mellon University taught by Deborah Brandon in Fall 2016. Since its upload, it has received 23 views. For similar materials see Calculus 1 in Mathematical Sciences at Carnegie Mellon University.

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Date Created: 10/01/16

Power Function: In the form y=a xb 2 4 4 2 Comparing the graphs of x and x , x is flatter than x when x is between -1 and 1 and steeper for the rest of the domain. Comparing the graphs of x and x , x is flatter than x 3 when x is between -1 and 1 and steeper for the rest of the domain. Any even root like √x is neither odd nor even because its domain doesn’t even include –x 1 Any reciprocal of an even root like √ x is even because f (−x)= f (x) 3 Any odd root like √ x is an odd function because f (−x)=−f (x) 1 Any reciprocal of an odd function like 3 is odd √x because f (−x)=−f (x) Polynomials: In the form: y = a · n + an n −1· xn −1+ … + a · x 1 a 0 The degree of a polynomials is the exponent of its largest exponent term. The sign of the highest order term will tell you the overall direction of the graph. If for some value x=p , f (p)=0 , we know that x−p f (x) must be a factor of the function . Rational Functions: P(x) o fx)= where P and Q are polynomials Q(x) o D (f={x∈R , Q(x)≠0 } Algebraic Functions: o Quotient of “polynomials” where powers can be any real # o Rational functions & polynomial functions are algebraic, but not all algebraic function are rational or polynomial Trigonometric Functions: In the form: y = a sin (b x + c) You can use graphs of sin and cos to help with values at different annles. Cosθ) =cos θ Sinθ)=sin θ 2 2 Sin θ+Cos θ=1 S∈(−x =−sin x becausesinisan odd function C o(−x =cos x)becausecosisaneven function o Example: C o(−3x+6π ) ¿cos−3x ) ¿cos(3x) Exponential Function: x In the form: y=a ,a>0 D(f)=(−∞ ,∞ ) R(f)=(0,∞) b plug∈time x¿ get measureof growth lob x plug∈growth¿getmeasureof time Logarithmic Function: In the form: y=log a D(f)=(0,∞) R(f)=(−∞,∞ )

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