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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
curvature - three dimensional spacein this part we want to briefly discuss the curvature of a smooth curve remind that for a smooth curve we require
optimization in this section we will learn optimization problems in optimization problems we will see for the largest value or the smallest
binormal vector - three dimensional spacenext is the binormal vector the binormal vector is illustrated to bebrarr t trarr t nrarr tsince the
unit normal vector - three dimensional spacethe unit normal vector is illustrated to ben t rarrt t trarr tthe unit normal is orthogonal or normal
demonstrates that f x 4 x5 x3 7 x - 2 has accurately one real rootsolutionfrom basic algebra principles we know that since f x is a 5th degree
the mean value theorem in this section we will discuss the mean value theorem before we going through the mean value theorem we have to cover the
utilizes the second derivative test to classify the critical points of the
tangent normal and binormal vectorsin this part we want to look at an application of derivatives for vector functions in fact there are a couple
smooth curve - three dimensional spacea smooth curve is a curve for which rarrr t is continuous and rarrr t ne 0 for any t except probably at the
determine or find out the domain of the subsequent functionrrarr t cos t ln 4- t radict1solutionthe first component is described for all ts the
domain of a vector functionthere is a vector function of a single variable in r2 and r3 have the formrrarr t f t gtrrarr t f t gt
vector functionswe very firstly saw vector functions back while we were looking at the equation of lines in that section we talked about them as we
level curves or contour curvesanother topic that we should look at is that of level curves or also known as contour curves the level curves of the