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Important formulas
d (ab )/ dx = 0 This is a constant
d ( xn ) / dx = nxn -1 Power Rule
d (a x ) / dx = a x ln a Derivative of an exponential function
d ( x x )/dx = x x (1 + ln x ) Logarithmic Differentiation
It is sometimes easy to get these several functions confused & use the wrong rule for differentiation. Always remember that each rule has extremely particular rules for where the variable & constants must be. For instance, the Power Rule needs that the base be a variable and the exponent are a constant, whereas the exponential function needs accurately the opposite.
If you can keep straight all of the rules you can't go wrong along with these.
steps to draw direction or slope fields
Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently a
what is 9/8
Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a
What is equivalence relation? Prove that relation 'congruence modulo' ( ≡mod m) is an equivalence relation. Ans: A relation R illustrated on a nonempty set A is said to be
Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,
us consider the following mass-spring-damper system: md2xdt2+cdxdt+kx=0 with m=5 kg as the mass of the body, k=1.6N/m as the spring constant and two different values of c.
3x2 +7x +4
fixed cost of $1400 ,printing cost of .40 cents -each item to sell for $1.05. what is linear cost function, linear revenue function and number of items to be sold to make a profit
2+(+3)=
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