Calculus Questions

Calculate the binomial coefficient 11CB

Find the area of the triangle having the indicated angle and sides Round your a B 125 a 94 c 39

Consider the function f x 12 Graph the exponential function by hand 0 5 4 Identity any asymptotes 300 250 200 150 100 300 250 200 150 100k 50

In the triangle below x 8 Use the Law of Cosines to solve the triangle Round your answers to two decimal places B 12 cm O O O B 18 cm x cm C

Use the Law of Sines to solve the triangle Let a 12 mm Round your answers for b and c to two decimal places O b mm mm b 350 C 55 a B

Solve the exponential equation 3x 9 X

Solve the logarithmic equation Round your answer to three decimal places log10 x 1133 X 1

Find the inverse function of f informally Verify that f f 1 x x and f f x f x 8 x 2 f 1 x X

6 15 Use the method of variation of parameters to find the general solution to the differential equation y 2y y x 1 ex No credit for any other method

pic 12 Quiz 1 0 Of g x dx converges Of g x dx diverges Of h x dx converges Of h x dx diverges

A high speed bullet train accelerates and decelerates at the rate of 10 ft s Its maximum cruising speed is 90 mi h Round your answers to three decimal places a What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes mi b Suppose that the train starts from rest and must come to a complete stop in 15 minutes What is the maximum distance it can travel under these conditions mi c Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart min d The trip from one station to the next takes at minimum 37 5 minutes How far apart are the stations mi

Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative F x 2 t t t

Find f f t 4 cost sec t 2 t 2 f 3 3

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 25 6

A stone was dropped off a cliff and hit the ground with a speed of 80 ft s What is the height of the cliff Use 32 ft s for the acceleration due to gravity ft

Find f f x 20x 12x 6 f x Question Help Message instructor f 0 2 f 1 0

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 24x 15x 8x f x

Find f f x 3 5x

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 10x sin z f x

1 Given a function of g x on 2 6 and g x 0 on 2 1 g x dx 10 g x 0 on 1 4 g x dx 4 g x 20 on 4 61 g x dx 6 estimate the following integrals 3 points each L g x dx D S Ig x dx A B 6 6 g x dx C lg x g x dx Ef g x dx E

5 7C5

6 8C6

3 4 The graph of a twice differentiable function is shown in the figure above Which of the following is true A 1 1 0 B 1 0 S 1 C 0 1 S 1 D 1 f 1 f 0 E I 0 1

1 2 3 6 700 6 2 W 4 70 3 1 5 g x 2 1700 J 6 3 N 0 2 The functions and g have continuous second derivatives The table above gives values of the function their derivatives at selected values of x a Let k x f g x Write an equation for the line tangent to the graph of k at x 3

110 Find the collision probability of 1200 bytes IEEE 802 11 FH packet at 2 Mbps and the Bluetooth Assume dwell period of an 802 11 transmission to be 3 ms and Bluetooth packet duration 0 625 ms What is PER with IEEE 802 11 DS

Orphof 9 Let be the function defined by f x cos 2x Leth be the function whose graph consisting of five line segments is shown in the figure above a Find the slope of the line tangent to the graph off at x H b Let k be the function defined by k x h f x Find k x

3 25 Points Consider the region R bounded by y rr 25 below A 09876132 5 4 1 1 the z axi 2 2 a Setup the definite integral including bounds of integration to find the volume found by rotating R around the x axis and use your calculator to compute that value rounding to two decimal places b Setup the definite integral including bounds of integration to find the volume found by rotating R around the y axis and use your calculator to compute the value rounding to two decimal Jogos

2 2 20 Points Find the following antiderivatives ln x

4 10 Points Find the anti derivative of 1 1 x 13 dx

1 10 Points Compute lim sin 4x 0 2x 2x

Using the left endpoint of each subinterval in a partition of 3 subintervals each of length 3 the approximate of by the corresponding Riemann sum is O a 8010 Ob 1345 O c 38007 1 10 2014 x 4 dx O d 4257

f x x 2x 15 xa q lim f x i X 3 find the lim

Example 8 Is the function given by f x x 1 for x 4 x 7 for x 4 continuous at x 4 Why or why not

x y 2 2 4x 2y 2z 5 r x 2 2 y 1 2 z Center 1 Answer 1 x 2 2 y 1 2 z 1 2 1 Answer 2 1 K

6 6 6 Evaluate log10 log100 log1000 log10000 in two different ways Explain your methods

7 Patrick was asked to write an expression equivalent to 2log3x w5 He came up with 6log3x 5log3w Determine if his expression is equivalent or not Explain your answer

Find the exact value of each expression 34 cos 1 35 sin 3 2

The federal tax rate for single filers is given as a percentage of taxable income in the graph below Find a C lim r x b lim r x x 9525 d x 9525 lim r x X 9525 lim r x x 50 000 Tax rate percentage 30 20 10 y r x 9 525 38 700 82 500 Taxable income in dollars 11

42 cos 0 1 44 tan 0

37 cos 7 2

Find the value of each trigonometric ratio 33 sin A A Z 36 35 cos Z B 15 C 39 28 35 Y 21 X 34 sin Z Z 24 25 Y 7 X Z 36 cos X 36 45 1 25 Y 27 X

Find the value of each trigonometric ratio 62 cos C 32 C B 64 tan Z Z 27 Y 40 24 45 36 A X 63 tan Z X 18 65 sin C C 14 B Y 30 24 50 48 Z A

Convert each radian measure into degrees 5 18 1 Convert each degree measure into radians 3 45 2 10T 3 4 300

1 point Show that A APBP 16 53 14 3 13 31 are similar matrices by finding an invertible matrix P satisfyin and B

Use the following graph of H to find each limit When necessary state that the limit does not exist lim H x X 2 a b lim H x X 2 c lim H x x 2 d lim H x x 1 e lim H x x r f limH x x 1 7 14 432 H 1 2 3 4 5

A cell receives nutrients through its surface and its surface area is proportional to the two thirds power of its weight Therefore if w t is the cell s weight at time t then w t satisfies w aw2 3 where a is a positive constant t Solve this differential equation with the initial condition w 0 7 initial weight 7 units w t 3 at 7 X

Use the Laws of Logarithms to combine the expression 7 log x 8 log x 1

Use the Laws of Logarithms to expand the expression log V 7x y 1 1 9 log 7 x log 7 y

Sketch the graph of the function by making a table of values Use a calculator if necessary Simplify your answers completely Round your answers to four decimal places h x 1 1 5 1 0 5 10 h x 1 1 15 10 y 15 10 5 5 10 15 10 15 X 15 10 15 10 y 5 5 10 15 5 10 15 X

Find f a f a h and the difference quotient f a h f a where h 0 h f x 9x 1 f a P f a h f a h f a h IE