Calculus Questions

2 2 1 2 cos 230 1 2 Drag each of the values given above in the appropriate area below to match with an expression 2 tan 15 1 tan 215 2 3 2 sin 30 cos 30 3 3 4 cos R00 6 2 8 T 5 4 sin COS 3 2 tan sin 1 tan 5k 12 3 5x 12 2 8 R

sin sin 5x ba 12 CID Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

Consider n independent trials of an experiment in which each trial has two possible outcomes success or failure The probability of a success on each trial is p and the probability of a failure is q p In this context the term nCk pkqnk in the expansion of p q gives the probability of k successes in the n trials of the experiment A fair coin is tossed eleven times To find the probability of obtaining six heads evaluate the term shown below in the expansion of Round your answer to three decimal places 11 11 6 5

Attempts Average 4 4 Taxes paid for a given income level Caroline is getting ready to do her taxes She is single and lives in Miami Caroline earned 250 000 in 2020 She reviews the following table which shows the IRS tax rates for a single taxpayer in 2020 On Annual Taxable Income Up to 9 875 From 9 875 to 40 125 From 40 125 to 85 525 From 85 525 to 163 300 From 163 300 to 207 500 From 207 500 to 518 400 The Tax Rate Is Percent 10 12 17 20 23 Caroline calculates that she owes approximately 30 Based on the IRS table Caroline calculates that her marginal tax rate is when her annual income is 250 000 in income taxes for 2020 Caroline then calculates that her average tax rate is approximately owes for 2020 based on the annual income level and the amount of taxes she After figuring out what she owes in taxes in 2020 Caroline decides to ask an accountant for tax advice The accountant claims that he has found a legal way to shelter 4 000 of taxable income from the federal government The maximum amount that Caroline is willing to pay to learn this strategy and reduce her taxable income by 4 000 is Sheltering some income means finding a legal way to avoid being charged income tax on that income For example someone who has 50 000 in Hint A

Find the indicated nth partial sum of the arithmetic sequence 3 12 21 30 n 25

Use this definition with right endpoints to find an expression for the area under the graph of f as a limit Do not evaluate the lin 7x x lim 1x n i 1 f x 1 x 3

Find the sum of the infinite geometric series if possible Round your answer to three decimal places If not possible enter IMPOSSIBLE 10 0 2 8 n 0

Determine whether or not the sequence is geometric If it is find the common ratio r If an answer does not exist enter DNE 3 4 5 6 5 7 9 11 O Yes the sequence is geometric O No the sequence is not geometric r

Find a formula for an for the arithmetic sequence a 21 d 7 an

Simplify the factorial expression 10 5 3

Use sigma notation to write the sum 1 1 1 2 4 32 n 0 1 1 1 8 Use a graphing utility to find the sum Round your answer to three decimal place

Write the first five terms of the geometric sequence 1 4 a1 a2 a3 a4 a5 a 5 r

Write an expression for the apparent nth term of the sequence Assume that n begins with 1 4 16 64 9 27 81 an 1 3

Rewrite cot 0 csc 20 csc 20 in terms of sine and cosine Simplify your answer

Perform the indicated operation below and simplify the result sin x CSC X COS X sec x COS X sec x sin x CSC X

Evaluate the integral by interpreting it in terms of areas L 3 81 x dx

Complete the table so that sin 0 is expressed in terms of the functions given across the top sin 0 cos 0 tan 0 cot 0 sec 0 tan 0 1 tan 0 1 tan 0 sin 0 1 cos 0 1 cot 0 1 cot 0 1 cot 0 1 cot 1 cot 0 csc 0 1 csc 0

5 4 3 2 1 2 3 Select the name of the toolkit function in the graph Select an answer Select the equation of the toolkit function in the graph Of x 2 Of t 2 Of x 10 Of x log z Of x 2 Of x x Of x x Give the domain of the function in the graph Give the range of the function in the graph

0 11 Points Use the midpoint rule with the given value of n to approximate the integral Round your answer to four decimal places 24 1 sin sin x dx n 4

rx f x dx lie Enter your answers from smallest to lar Suppose f has absolute minimum value m and absolute maximum value M Between what two values must Which property of integrals allows you to make your conclusion F x dx F x dx F x dx O F x dx F x dx O If f x 0 for a x b then If m f x M for a x b then m b a s 0 f x dx 0 Need Hein Read it f x dx 0 Metal It f x dx M b a

If m f x M for a x b where m is the absolute minimum and M is the absolute maximum of f on the interval a b then b F x Use this property to estimate the value of the integral s m b a smaller value larger value f x dx M ba 5 tan 3x dx

If f x ex 7 0 x 2 find the Riemann sum with n 4 correct to six decimal places taking the sample points to be midpoi MA

Question Graph the Logarithmic Function y log z by plotting the Horizontal Intercept and one other point Clear All Draw S 9 LOO 9 10

Express the integral as a limit of Riemann sums using right endpoints Do not evaluate the limit 1 x x dx lim n 00 n 1 1

The graph of f is shown a b c d e 6 Evaluate each integral by interpreting it in terms of areas 6 21 15 14 0 f x dx 15 5 f x dx 21 h 2 h F x f x dx f x dx 6 If x dx y f x 12 18 24

Click here to watch the video Establish the identity 1 sin 0 1 sin 0 OB O C tan 0 sec 0 Starting with the right side which shows the key steps in establishing the identity O A O D tan 0 sec 0 tan 0 sec 0 H 2 sin 0 2 cos 0 sin 0 2 cos 0 2 2 sin 0 cos 0 2 sin 0 2 cos 0 tan 0 sec 0 tan 0 sec 0 tan 8 sec 0 tan 0 sec 0 2 by workin DOC 1 Cos 0 1 cos 0 sin 0 1 2 1 sin 0 sin 8 1 20 1 cos sin 0 1 1 sin 0 2 sin 0 1 2 1 cos 0 1 sin 0 1 sin 0 1 sin 0 1 sin 0 Sant 1 sin 0 1 sin 0 1 sin 0 1 sin 0

Watch the video that describes rewriting an expression in terms of sine and cosi Click here to watch the video Write the expression in terms of sines and or cosines and then simplify cot x sin x cotx sin x

a Estimate the area under the graph of f x 5 x from x 0 to x 4 using four approximating rectangles and righ endpoints Round your answers to four decimal places R

Evaluate the integral by interpreting it in terms of areas x 2 dx

Write the following expression as a single definite integral of the form 3 R x dx x dx x dx f x f x dx F x f x dx

Evaluate the integral by interpreting it in terms of areas dx

Use the Binomial Theorem to approximate the quantity accurate to three decimal places 2 007 10

Use the Binomial Theorem to expand and simplify the expression x y2 4

Use the Binomial Theorem to expand and simplify the expression 2 x 3 4 4 x 3

in 4 0 n 2 anthmetic O geometric Find the common difference or ratio 1 2 Find the sum of the first 15 terms 67 5 Need Help Submit Answer rose neintel Read DETAILE DREBOUE ONEINERE LARD 783097 MY

If f x dx 9 1 and f x dx 5 6 find f x dx

Write in Polar form r cos 0 i sin 0 0 0 2 and round to 3 decimal places 17 4i T 0

Find the coefficient a of the given term in the expansion of the binomial Binomial 4x 3y 8 a Term axyA

A trough has a trapezoidal cross section with a height of 7 m and horizontal sides of width 7 2 m and 7 m Assume the length of the trough is 14 m See the figure to the right Complete parts a and b below MICKERS 7 m 7 m 3 5 m 14 m a How much work is required to pump the water out of the trough to the level of the top of the trough when it is full Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity Draw a y axis in the vertical direction parallel to gravity and use the midpoint of the bottom of one edge of the trough as the location of the origin For Osy 7 find the cross sectional area A y in terms of y A y Simplify your answer Use integers or fractions for any numbers in the expression

Find the specified nth term in the expansion of the binomial x 10z n 5

A heavy duty shock absorber is compressed 4 cm from its equilibrium position by a mass of 700 kg How much work is required to compress the shock absorber 8 cm from its equilibrium position A mass of 700 kg exerts a force in newtons of 700g where g 9 8 m s Set up the integral that should be used to find the work required to compress the shock absorber 8 cm from its equilibrium position Use decreasing limits of integration Express all displacements in meters 2 8x10 1 715x105 y dy 0 Type exact answers

Use a graphing utility to find nCr 550C547

Use Pascal s Triangle to find the binomial coefficient 5C2

Calculate the binomial coefficient 5

A swimming pool has the shape of a box with a base that measures 26 m by 19 m and a uniform depth of 2 9 m How much work is required to pump the water out of the pool when it 3 is full Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity Points 0 of 1 Draw a y axis in the vertical direction parallel to gravity and choose one corner of the bottom of the pool as the origin For 0 y 2 9 find the cross sectional area A y A y Simplify your answer Save

Find the sum of the infinite geometric series if possible Round your answer to three decimal places 7 0 55 STEP 1 Determine the first term of the infinite geometric series n o STEP 2 Find the common ratio of the infinite geometric series STEP 3 Based on your results from Step 1 and Step 2 the Sum of an Infinite Geometric Series Formula may be applied to this series What guarantees the formula will work in this The common ratio is less than the first term of the series The first term of the series is positive The first term of the series has an absolute value less than 1 O The common ratio has an absolute value less than the first term of the series The first term of the series has an absolute value greater than the common ratio The common ratio has an absolute value less than 1 The common ratio is less than one STEP 4 Compute the sum of the series using the Sum of an Infinite Geometric Series Formula Round your answer to three decimal places S

How much work is required to move an object from x 1 to x 6 measured in meters in the presence of a force in N given by F x Set up the integral that gives the work done 6 3 dx Type exact answers The work is Type an integer or a simplified fraction 32x acting along the x axis

Use summation notation to write the sum 1 9 3 1 27 6 X

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the y axis y 4 2x 2x y 0 and x 0 in the first quadrant Set up the integral that gives the volume of the solid using the shell method Use increasing limits of integration Select the correct choice below and fill in the answer boxes to comple your choice Type exact answers OA SO O B dx JO dy

A deposit of 100 is made at the beginning of each month in an account that pays 2 interest compounded monthly The balance A in the account at the end of 6 years is given by A 100 1 0 02 100 1 0 02 Find A Round your answer to the nearest cent A