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question a explain why the following equation has a solution near 0et 002t 1098b replace et by its linearization near
question the saint louis arch can be approximated by using a function of the form y b - a coshxa putting the origin on
question a find tanh 0b for what values of x is tanh x positive negative explain your answer algebraicallyc on what
question a using a calculator or computer sketch the graph of y 2ex 5e-x for -3 le x le 3 0 le y le 20 observe that
question 1 describe and explain the behavior of sinh x as x rarr infin and as x rarr -infin2 if x cosh t and y sinh t
question give an example of1 a hyperbolic function which is concave up2 a value of k such thatlimxrarrinfin ekxcosh x
question 1 find the local linearization of fx x2 near x 12 what is the local linearization of ex2 near x 13 show
question a find the best linear approximation lx to fx ex near x 0b what is the sign of the error ex fx - lx for x
question a find the tangent line approximation to cos x at x pi4b use a graph to explain how you know whether the
qestion a graph fx x3 - 3x2 3x 1b find and add to your sketch the local linearization to fx at x 2c mark on your
question a show that 1kx is the local linearization of1x k near x 0b someone claims that the square root of 11 is
question a find the equations of the tangent lines to the circle x2 y2 25 at the points where x 4b find the
question a if x3 y3 - xy2 5 find dydxb using your answer to part a make a table of approximate y-values of points on
question 1 sketch the circles y2 x2 1 and y2 x - 32 4 there is a line with positive slope that is tangent to both
question 1 a find dydx given that x2 y2 - 4x 7y 15b under what conditions on x andor y is the tangent line to this
question 1 a formula for dydx leading to a vertical tangent at y 2 and a horizontal tangent at x plusmn22 a curve
question 1 show that the power rule for derivatives applies to rational powers of the form y xmn by raising both sides
question at a particular location fp is the number of gallons of gas sold when the price is p dollars per gallona what
question to compare the acidity of different solutions chemists use the ph which is a single number not the product of
question the number of years t it takes an investment of 1000 to grow to f in an account which pays 5 interest
question a firm estimates that the total revenue r in dollars received from the sale of q goods is given byr ln1
question a find the equation of the tangent line to y ln x at x 1b use it to calculate approximate values for ln11
question a find the equation of the best quadratic approximation to y ln x at x 1 the best quadratic approximation
question if k ge 1 the graphs of y sin x and y ke-x intersect for x ge 0 find the smallest value of k for which the
question find the equations of the tangent lines to the graph of fx sin x at x 0 and at x pi3 use each tangent line