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an apartment complex contains 250 apartments to rent if they rent x apartments then their monthly profit is specified by in
proof for properties of dot productproof of urarr bull vrarr wrarr urarr bull vrarr urarr bull wrarrwell begin with the three vectors urarr u1 u2
business applicationsin this section lets take a look at some applications of derivatives in the business world for the most of the part these
use newtons method to find out an approximation to the solution to cos x x which lies in the interval 02 determine the approximation to six
newtons method if xn is an approximation a solution of f x 0 and if given by f prime xn ne 0 the next approximation is given
compute the dot product for each of the subsequent equation a vrarr 5irarr - 8jrarr wrarr irarr 2jrarr b ararr 0 3 -7 brarr 2
dot product- vector the other topic for discussion is that of the dot product let us jump right into the definition of dot product there is given
proof of the properties of vector arithmeticproof of avrarr wrarr avrarr awrarrwe will begin with the two vectors vrarr v1 v2 vnand w w1 w2
properties of vector arithmeticif v w and u are vectors each with the same number of components and a and b are two numbers then we have then
standard basis vectors revisited in the preceding section we introduced the idea of standard basis vectors with no really discussing why they were
determine or find out if the sets of vectors are parallel or nota ararr 2-41 b -6 12 -3b ararr 410 b 29solution a these two vectors are parallel
parallel vectors - applications of scalar multiplicationthis is an idea that we will see fairly a bit over the next couple of sections two
determine dy amp deltay if y cos x2 1 - x as x changes from x 2 to x 203 solutionfirstly lets deetrmine actual the change in y deltay
determine the differential for determine the differential for
differentials in this section we will introduce a notation we will also look at an application of this new notationgiven a function y f x we call
scalar multiplication - vector arithmeticanother arithmetic operation that we wish to look at is scalar multiplication specified the vector ararr a1
components of the vectorwe should indicate that vectors are not restricted to two dimensional 2d or three dimensional space 3d vectors can exist
standard basis vectorsthe vector that is i 1 00 is called a standard basis vector in three dimensional 3d space there are three standard basis
unit vector and zero vectors unit vectorany vector along with magnitude of 1 that is urarr 1 is called a unit vectorzero vectors the vector wrarr
magnitude - vectorthe magnitude or length of the vector vrarr a1 a2 a3 is given byvrarr radica12 a22 a23 example of magnitudeillustration
if a1a b1bc1cd1d are four distinct points on a circle of radius 4 units thenabcd is equal to ans as they are of form x1xlet eq of circle be
identify the surface for each of the subsequent equationsa r 5b r2 z2 100c z rsolutiona in two dimensions we are familiar with that this is a
determine if the acceleration of an object is given by ararr irarr 2 jrarr 6tkrarr find out the objects velocity and position functions here given
velocity and acceleration - three dimensional spacein this part we need to take a look at the velocity and acceleration of a moving
method to determine solution is absolute minimummaximum valuelets spend a little time discussing some methods for determining if our solution is in