Calculus for life science exam 1 review
Calculus for life science exam 1 review Math 23100
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This 4 page Study Guide was uploaded by Mikaela lake on Friday September 16, 2016. The Study Guide belongs to Math 23100 at Indiana University Purdue University - Fort Wayne taught by Prof. Arciero in Fall 2016. Since its upload, it has received 39 views. For similar materials see Life Health Sciences Calculus in Math at Indiana University Purdue University - Fort Wayne.
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Date Created: 09/16/16
1)What needs to be true in order for a graph to be continuous at a certain point? −¿ x→0 f (x) lim ¿ 2) A ¿ = ¿ +¿ x→0 f (x) B. lim ¿ = ¿ ¿ lim ¿ C. f (x)= x→0 ¿ lim ¿ D. x→4 f (x)= ¿ lim ¿f (x) E x→2 = ¿ 3) Where is f(x) continuous? 4) What are the three ways to find a limit?(know how to do them) 5) Define secant line: +2 x¿ 6) Find secant line for f(x)¿ from x=2 to x=5 ¿ 7) Define tangent line: 8) Find the tangent line for f(x)= x −5 9) What is the formal definition (equation) of derivative? 10) What are some notations for the derivative of a function? 2 11) Using the formal definition of derivative find the derivative of f(x)= 2x❑ +4 12) Using the shortcuts find the derivative to x❑ +3x❑ − x+5 √ 13) f(x)=cos(x) find f’(x) 14) f(x)= |x| find f’(x) 15) if position is given by s(t)= 4 2 , what is the velocity and acceleration 3t❑ −5t +t−5 equations? 16) Find d/dx [f(x)g(x)] when f(x)= x2 and g(x)= x2 (product rule) d g(x) 17) Find [ ] when f(x)= 3x +9 and g(x)= 2x +4x +22 (Quotient rule) dx f (x) 5 3 4 18) Find f’ when f(x)= 3( x −2x +6x+4¿ (chain rule) 19) find f’(x) when f(x)= √ x(5x ) 9x −2x +6x +7x −5x+8¿ 3 20) find f’(x) when f(x)= 4x¿ Answer key 1: lim ¿ f(x) must exist, f(a) must be defined, and lim f (x) =f(a) x →a x→a 2: a)0 b)3 c) DNE d) DNE e)3 3) ( ∞ , 0), [0,4], (4∞¿ 4) Numerically(T chart to find values leading up to limit), graphically(looking at a graph) and algebraically(direct substitution) 5)Secant line= the average rate of change between two points on f(x). Also defined by Δ y f (a+h)− f (x) the difference quotient = Δx h 6) y=11x6 lim f (x+h)− f (x) 7) Instantaneous rate of change. Also defined as h→0 h 8) 2x lim f (x+h)− f (x) 9)same as a tangent line h→0 h 10)f’(x), d ,df , y’, Df dx dx 11) 4x 3 1 12) 4 x +6 x− 2 √ 13) sin(x) 14) DNE, any sharp points make the equation indifferentiable 15) v(t)=12t −10t+1 a(t)=36t −10 16) 3x −4x 2 x+3¿ 3¿ 17) 3 2 2(2 x +11x +12x−1) ¿ 5 3 3 4 x −2x +6x+4¿ (5x −6x+6) 18) 12¿ 19) 9 x 7/2 2 9x −2x +6x +7x −5x+8¿ (45x −8x +18x +14x−5) 3 2 20) 12x¿
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