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# MA 161 Final Exam Study Guide MA 161

Purdue

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This 4 page Study Guide was uploaded by Zack Bales on Monday May 2, 2016. The Study Guide belongs to MA 161 at Purdue University taught by Dr. Mummert in Spring 2016. Since its upload, it has received 171 views.

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Date Created: 05/02/16

MA 161 Exam Study Guide Y=f(a)+f’(a)(x-a) equation of tangent line lix a f(x)-f(a) / x-a = lih 0 f(a+h)-f(a) / h If f is differential at a then f is continuous at a Prevents differentiability o Discontinuity o Sharp corner o Vertical tangent Power Rule p p-1 o d/dx (x ) = px Constant multiple rule o d/xx (C *xf(x)) = C * d/dx (f(x)) d/dx (e ) = e Product Rule o d/dx (f(x) g(x)) = f(x) g’(x) + g(x) f’(x) Quotient Rule o d/dx (f(x) / g(x)) = f(x) g’(x) - g(x) f’(x) / g(x)2 Chain Rule o d/dx [f(g(x))] = f’(g(x)) * g’(x) o d/dx (g(x) ) = p(g(x)) p-1g’(x) Implicit Differentiation o d/dx (x +y = 1) o 2x+2yy’=0 o 2yy’= -2x o yy’ = -x o y’ = -x/y Y as a function of time o y’ = ky o p(t) = p e0 kt Newtons Law of Cooling o dT/dt = k(T-Ts) Half Life o K = ln(1/2) / t 1/2 Related Rates 1. Draw Picture 2. Label (variable = changing) 3. Equation 4. Chain rule with respect to time 5. Unknown/plug in Linear Approx o L(x) ≈ f(a) + f’(a) (x-a) o x = what you want to find o a = known exact Max and Mins o f’(x) = 0 local max or min o Extreme Value Theorem If f is continuous on [a,b] then f has a max or min on (a,b) o Mean Value Theorem f is continuous [a,b] f is differentiable (a,b) then there exists a number between a and b where f’(c) = f(b)-f(a) / b-a Curve Sketching o f’ + - 0 o f inc dec constant o f’’ + - 0 o f’ inc dec const o f conc up conc dwn linear First Derivative test o Find f’ o Find critical numbers o f’ is either + or – o if f’ – to + f has min o if f’ + to – f has max Inflection point o Where f’’ sign changes + to – or – to + o f’’ = 0 L’Hospital’s Rule o Indeterminate form (0/0 ꝏ/ꝏ) o Take limit of f’(x) Optimization o Picture o Variables o Equations o Function of one variable o Calc Antiderivative o F is antiderivative of f o F’ = f o F’(x) = f(x) + C Riemann Sum o Approx area of n rectangles Fundamental Rule of Calculus 1 o Fundamental Rule of Calculus 2 o Integration by Substitution 1. Choose inner function 2. Find u’(x) u’(x) dx 3. Substitute u for x 4. Integrate 5. Replace u with x

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