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find the taylors formula for estimation of cosine functionuse tayors formula for fx cos x - x-x2 13x- x23nbsp- 15x-x25nbspnbsp to estimate cos
root test for convergence of geometric seriesuse the root test to show that a geometric series converges only if its ratio has absolute value less
find the relative growth rateassume the relative growth rate is a linear function of population at timenbsptnbspby using the formula nbsp 1pdpdt b
solving differential equations with initial conditionshow much would it cost to solve this onesuppose organisms grow in mass according to the
differential equations with initial conditionsfor the following description of a cell write a differential equation find and graph the solution and
solving on numerical method - euler methodsapply eulers method to the following differential equation to estimate the solution at t 1 starting from
application of calculus-optimization problemtwo vertical poles pq and st are secured by a rope prs going from the top of the first pole to a point r
integrating a differential equation given the initial valuesa --00001275204323b 0033810412806466when timet is zero population is 39differential
compactnesssuppose k is compact set prove that k is of content zero if and only if is of measure zero give a counter example if the compactness
series convergencea prove using the definition that the following sequence convergerradicnn 1b using the definition of a limit of a function to
calculus - sequences and series tests of convergenceuse the root test to show that a geometric series converges only if its ration has absolute value
integration by parts methodusing integration by parts evaluate nbspintx cos3x dx check your answer by taking the derivative suppose the mass w of a
summation and proof using mathematical inductionsuppose that xn is a sequence of positive real numbers for which the sum from i1 to n of xi3nbsp
derivative of the natural logarithm by using the fundamental theorem of calculusto find the derivative ofnbspynbsp lnnbspxnbspnbspthis solution below
determine accumulated rates of change using definite integralgive another example with solutions to emphasize that the definite integral can be used
change into symbolic notationtranslate the following into symbolic notation use for negation amp for conjunction v for disjunction gt for
find the nth term of the given sequencesnbsp1write out the nth term for the continuation of the
evaluate the coordinate of centroid using multiple integral methodlet t be the region inside the sphere x2nbsp y2nbsp z2nbsp 1 for x ge0 yge0 and
find coordinate of centroid using multiple integral methodlet g be the three dimensional region above the paraboloid z x2nbsp y2nbspbut below the
show the mass as triple integral and solve the integral using spherical polar coordinatelet b be the three dimensional region below the sphere z
determine the multiple integral under given condition using spherical coordinatelet g be the three dimensional region inside the sphere x2nbsp y2nbsp
evaluate the multiple integral under given condition using spherical coordinatelet t be the three dimensional region that lies outside the sphere
find the multiple integral under given condition using cylindrical coordinateevaluate the triple integral intintintgnbspradicnbspx2nbsp y2nbsp z2 dv
application of differentiation and integration on real world problemduring the summer the temperature inside a van reaches 550c while that outside is
evaluate the dimensions of the rectangle of maximum area that can be inscribed in a ellipsemaximum area find the dimensions of the rectangle of