Calculus Topics

Use transformations to graph the function Determine the domain range horizontal vertical asymptote and intercept s of the function a h x 2e x 1 b f x log x 5 1

Next question The function f x 8x 5x has one local minimum and one local maximum Algebraically use the derivative to answer the questions Leave answers in 4 decimal places when appropriate this function has a local maximum at x with value 32 Get a similar question You can retry this qu and a local minimum at x 1 5 21 2 X 1 5 2 2 OF

Get a similar question You can retry this quest I 1 4 HHH 2 2 Give the ordered pairs in decimal form and separate with commas if necessary Point s of inflection 40 14

A tank contains 5000 L of pure water Brine that contains 30 g of salt per liter of water is pumped into the tank at a rate of 25 L min C t 30t 200 t A After how many minutes will the salt concentration be 20 grams per liter B State the equation of the horizontal asymptote and explain what it is telling you in this context

54 5 2 3 The function graphed above is decreasing on the interval X x 2 X The inflection point is at x 5 5 X

Use sigma notation to write the Maclaurin series for the function COS TIX

10 a b Find the Taylor polynomial P4 for f x In x at xo 1 1 x 1 x 1 x 1 x 1 1 1 x 1 x D x 1 x 1 c x 1 x 1 x 1 x 1 1 d x 1 x 1 x 1 x 1

The series a c 2 2 Converges absolutely Diverges b Converges conditional

Find the sum of the series a c 2 10 IMB b d 3 315 11 10

Find the local quadratic approximation of f x x at xo 1 and use that approximation to find the approximation of 1 03 a 1 092727 b 1 0927

4 3 2 Add Work 1 q The function graphed above has an inflection point x

2 Use sigma notation to write the Taylor series about Xo 1 for Inx

Determine whether the series converges k 1 k 2 a Converges b Diverges

di 4 H 2 2 Give the ordered pairs in decimal form and separate with commas if necessary 1 4 dr 54

2 Determine whether the series a Converges b 5 32 converges or diverges Diverges

c 00 5 x 3 2 k k 0