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MATH 154: Week 13 Lecture 3 -to derive inverse trigonometric functions, use implicit differentiation -y = arcsin(x), and sin(y) = x -so sin = = 1 -cos = 1 1 1 - = = 2 cos() 1 -we cant leave cos(y) as it is, since we want t...
MATH 154: Week 13 Lecture 2 -with plot-space diagrams, we need to include a graph a table -we should be able to draw parabolas (for exams) - + = 1 2 2 - 2 + 2 = 1 2 2 - 3 + 3 = 1 -sin + sin + sin() -sin + = sin cos + sin ...
MATH 154: Week 7 Lecture 3 -for the logistic growth equation = ( ), r is the intrinsic growth rate -K is the carrying capacity, or the maximum population density ...
MATH 154: Week 13 Lecture 1 -the functions sin and cos are periodic with period 2 because: -sin 2 + = -cos 2 + = - = sin( + 2) for any value of k that is an integer -this goes for cos as well -trig functions are not invert...
MATH 154: Week 12 Lecture 3 -with the logistic growth function = ()(1 ), it is first order non-linear -in trigonometry, the functions sin and cos are defined by the fact that (cos, sin ) are the coordinates of a point on ...
MATH 154: Week 12 Lecture 2 - tells us about the slope of a function -when slope is 0, the tangent line is horizontal -the slope field shows the tangent lines of the original curve, so it gives information about the shape ...
MATH 154: Week 12 Lecture 1 -the final is going to be about 20 material from the first midterm, 20 material from nd nd the 2 midterm, and 60 material from after the 2 midterm -with the equation = ,) is proportional to the ...
MATH 154: Week 8 Lecture 1 -with many optimization problems, there are 2+ variables and additional constraints -with these problems, we must use the constraints to reduce the function to 1 variable, then solve -eg. find th...
MATH 154: Week 11 Lecture 2 - () = 5 5 -( )= 5 -( )= -the rate of change of this function is proportional to itself -if we have = with y(0) = y 0 then = 0 5 -eg. if = 5 with y(0) = 100, then = 100 -solving differential equ...
MATH 154: Week 11 Lecture 1 x -we know that for the function y = e , it satisfies = -a differential equation is an equation where both sides are functions (funct...
MATH 154: Week 7 Lecture 1 -a function f(x) has a local minimum at a point if the value of f at that point is smaller than the value of f at all nearby points -a function f(x) has a local maximum at a point if the value of...
MATH 154: Week 6 Lecture 2 -on which intervals is = 92positive? ( 1) (+1)(1) -first factor it; (3)(3+) (3)(3+) -f may change value at any point where it is 0 or undefined sign of -3 -1 0 1 3 x - - - + + + x-1 - - - - + + x...
MATH 154: Week 2 Lecture 3 -a limit is a value you hope to get (may not get that value); very important concept for calculus -right-hand & left-hand limits may be different -a limit at a exists if & only if both left-ha...
MATH 154: Lecture 2 1 - or is not a polynomial, because it does not have an integer exponent -power functions, polynomials, and rational functions all have many uses in the life sciences domain: for a function, the set of ...
MATH 154: Week 10 Lecture 2 x -e and ln(x) are the inverse of each other ln() - ln )) = = - ln )= ln( ) ln() -for ...
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