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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.
Definition of limit : Consider that the limit of f(x) is L as x approaches a & write this as provided we can make f(x) as close to L as we desire for all x adequately clos
-255=-14t-t
using a pair of compasses a ruler and a pencil. construct a triangle CDE in which DE=10cm, DC+8cm and CDE= 45 degrees. construct CF perpendicular to DE such that F lies on DE using
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Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i
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tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its given 1 - tan2x*tan7x= 0 implies tan9x = infinity since tan9x = (3tan3x - tan^3(3x))/(1 - 3tan^2 (3x)) = infinity implies
Derive for the filter from z=a and poles at z=b andz=c, where a, b, c are the real constants the corresponding difference equation. For what values of parameters a, b, and c the fi
The population of Hamden was 350,000 in 1990. By 2000, the population had decreased to 329,000. What percent of decrease is this? First, ?nd out the number of residents who lef
Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign. The meaning of this is that we can then say, 0 a n +
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