Calculus Questions

2 Find the area of the region cut from the first quadrant by the curve r 2 2 sin 20 A 0 Typo an oxnot

JU 2 the region of integration and convert the polar integral to a Cartesian integral or sum of integrals Do not evaluate the integral 00 sin 0 cos 0 dr de Sketch the region of integration Choose the correct graph below VENTA AY 3 O SS 0 0 B The Cartesian integral can be written as a single integral dy dx SS 10 Convert the polar integral to a Cartesian integral or sum of integrals Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers A The Cartesian integral cannot be written as a single integral Q Q 2 dy dx B Q Q OD Ay Q S

Calculate the work in Joules to empty a tank full of water through the top knowing the shape and position of the tank cylinder of radius 5 m positioned horizontally along a stretch of 10 m

etch the region of integration and convert the polar integral to a Cartesian integral or sum of integrals Do not evaluate the integral K21 SS 00 sin 0 cos 0 dr do ketch the region of integration Choose the correct graph below Ay 0 5 0 dy dx V 0 0 3 Ay 12 Q Convert the polar integral to a Cartesian integral or sum of integrals Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA The Cartesian integral cannot be written as a single integral Q Q 5 Q G

Find the volume of the region common to the interiors of the cylinders x y 9 and x z 9 one eighth of which is shown in the accompanying figure V Simplify your answer X N x y x

If the terminal side of angle A goes through the point 25 V5 on the unit circle then what is cos A Provide your answer below

If the terminal side of angle 0 goes through the point Provide your answer below 5 5 2 5 5 on the unit circle then what is cos 0

Consider the following polynomial function Step 2 of 2 Sketch the graph by identifying where the graph is positive and where the graph is negative Answer r x x 2x 8 Reset Select the area above the axis to plot the positive curve for that region and select the area below the axis to plot the negative curve for that region Use the remove all curves 10 45 A5 15 K Enable Zoom Pan

Find an angle A that is coterminal with an angle in radians measuring where 0 A 2 Give your answer as a exact answer involving if necessary Jour

For the given differential equation y 0 0 5 initial condition and y 0 4 value is desired to be calculated by Heun s method Which of the following is correct for the calculation step dy dx y x 1 k2 1 1 dir Two iterations are required for the solution y 0 4 1 188 dir y 0 4 1 36 d r k1 1 25 dir k2 1 94 d r k1 1 5 dir

If the terminal side of angle 0 passes through a point on the unit circle in the first quadrant where x 0 what is the exac measure of 0 Provide your aprwer holow

interpolation coefficients required to calculate the derivative at 0 7 X 0 1 0 4 0 7 1 1 3 1 6 1 9 2 2 f x Sy 1 2 y 3 6 7 9 13 14 22 24 9 1 O 7 1 1 1 8 2 4 1 8 2 1 5 115 8 8 1 2 3 7 O 1712 1 2 1 5 15 38 O2 1 2 1 5 15 38 6 8 y 1 2 S y 9 1 5 10 13 8 6 15 23 85y 1 2 2 21 38

54 h 011 for 45 05 30 0 5 I 45 joto ye x 125 dy dx 30 H and H Solve by Simpson 1 3 rule

Find the average distance from a point P x y in the disk x y 25 to the origin The average distance is Simplify your answer

Evaluate the integral 2t S S e dx dt dv In sec v 3 In sec v 2t ITI D Se ex dx dt dv 8 00 0 0 Type an exact answer using and radicals as needed

Evaluate the integral 81 x 81 x 0 0 0 9 81 x 81 x 0 0 dz dy dx 0 dz dy dx

Evaluate the following integral 4 5 5x 5 5x y I T 0 0 0 4 5 5x 5 5x y SS C dz dy dx dz dy dx Simplify your answer

244 2 Evaluate the integral x y 2 dz dy dx S S S 000 2 4 4 S S S x y z dz dy dx 0 0 0

Describe the given region in polar coordinates such that 0srand 0 0 2 0s srs 0 Type exact answers using T S Poded 10 10 10 10

A woman is walking along a sidewalk cleaning up litter and once her bag is full she walks back to where she started On the way out while gathering litter she moves at 8 feet per minute On the way back she walks much faster at 80 feet per minute If the whole trip took 1 hour how far did she go from her starting point

8 points Find a polynomial function h x of least degree 3 having only real coefficients and zeros as given Assume multiplicity 1 and leading coefficient 1 Don t leave the answer in factor form Zeros of 1 and 4 2i

54 8 928 2 5 669 6 Question 17 Five Steel Parts weigh 2 5 lbs How many of these parts are in a box weigh lbs 69 84 68 50

Now TT 3 2 0 sin 2017 2 sin sin 1 4 After simplifying we have SEP 2 10 dt 2 T

We have 1201031 23 1 1 cos 20 de sin 4

Part 5 of Since we have an even power of cos x to evaluate cos 0 Submit Skip you cannot come back cos 3 cos2 e de we must now make the further substitution 0 J 4

Using t sec 0 we get 2 1 1 2 P 1 J 4 This can be further simplified to T 3 J 4 or simply T 3 A J 4 dt sec 8 cos 0 de TT 3 de sec 0 tan 0 sec 0 tan O de

1 Determine the corresponding squared conversion statements for each conversion a 1760 yards 1 mile b 5280 feet 1 mile c 1 yard 0 9144 m c 2 Determine the corresponding cubed conversion statements for each conversion a 1 ft 30 48 cm d 1000 m 1 km b 1 mile 1 609 km I d 100 mm 1 cm 12 inch 1 foot

Since SEP 1 With this we get dt dt contains the expression t2 1 we will make the substitution t sec 8 de

1 point Consider the function x X f x X Find the vertical asymptote s If there is more than one vertical asymptote give a list of the x values separated by commas If there is no vertical asymptote type in None 10x 21 7 X If this function has a horizontal asymptote give its y value If there is no horizontal asymptote type in None Find the y intercept Find the x intercept s If there is more than one x intercept give a list of the x values separated by commas

Write out the form of the partial fraction expansion of the function Do not determine the numerical values of the coefficien 2x a x 2 3x 1 b X x3 14x 49x X

1 point f x 7x 21x 21x 8x 2x 4 x 3x 6x 8x 2 What is the equation of the horizontal asympotote y Does the graph of f x intersect its horizontal asymptote yes or no At what x values does f x intersect its horizontal asymptote Give your answers in increasing order If f x does not intersect its horizontal asymptote leave this question blank

Evaluate the integral 1 t sin 4t dt C

Evaluate the integral 14 4xe 3x dx X C

Evaluate the integral using integration by parts with the indicated choices of u and dv 1 2x In xdx u ln x dv 2x dx C

dz Consider the equation 4 sin x y 5 sin x z 5 sin y z 0 Find the values of and ox dz Ox 2x 21 2x Simplify your answer Type an exact answer using radicals as needed dz dy at the point 2 2 2

Find the values of and at the given point dy 2z 5xy 5yz 3y 19 0 2 1 2 2 1 2 Type an integer or a simplified fraction

dw For the given functions a express as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t dt Then b evaluate dw dt at the given value of t 2 2 w 4x 10y x cost y sint t 3 dw a Express as a function of t dw dt

For the given functions a express dw dt w z sin xy x 2t y ln t 4 z e 5 t 5 Then b evaluate dw as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect dt a Express as a function of t dw dt dw at the given value of t

For the function f x y af 9 D1 7 2 x 6y of find and dy

Factor out a factor with a negative coefficient 4y 4 12y 3 20y 24

The given central difference table is generated from a polynomial Which of the following is true about this polynomial X 0 0 2 0 4 0 6 0 8 1 1 2 1 4 f x 0 0 92 1 36 0 84 1 12 5 11 28 20 44 8y 1 2 8 y 0 92 0 44 0 52 1 96 3 88 6 28 9 16 0 48 0 96 1 44 1 92 2 4 2 88 8 y 1 2 0 48 0 48 0 48 0 48 0 48 84y 0 0 0 0 polynomial degree 4 coefficient of lowest degree term 0 polynomial degree 3 coefficient of the highest degree term 10 C polynomial degree 4 coefficient of the highest order term 10 polynomial degree 3 coefficient of lowest degree term 0 48

3 Solve by completing the square x 6x 77 0 4 Solve the following

20 UN Security Council never votes to use military power against another memb True or False Reading UN Funds Programs and Specialized Agencies False

4 Use the following information to calculate MST x 8 86 X 7 96 s 4 24 s 3 86 s 3 5 6 Round your answer to the nearest thousandths Answer X3 8 40 n 18 n 16 n3 20

Determine the convergence or divergence of the series using any appropriate test from this chapter Identify the test use 00 cos n 20 n 1 converges by the Direct Comparison Test O diverges by the Alternating Series Test diverges by the Direct Comparison Test

00 n 0 a n converges if lim 7 8 True O False 2 Click here to view the transcript 1 n 1 an

Find the limit Let m and n represent arbitrary real numbers x m 2 x nx lim X 00 m n 2 mx

Use the Ratio Test to determine the convergence or divergence of the series If the Ratio Test is inconclusive determine the convergence or divergence of the series using other methods If you need to use co or co enter INFINITY or I respectively lim n 1 converges O diverges n 45 1 4

Find the limit T 1 lim X 9 e 9 8e

Use the function below to answer parts a and b 19 f x 4x 2 5x on 2 2 a Find the critical points of the function on the given interval The critical point s occur at x Simplify your answer Use a comma to separate answers as needed Type an exact answer using radicals as needed b Use a graphing utility to determine whether each critical point corresponds to a local maximum local minimum or neither Select the correct choice below if necessary fill in the answer box to complete your choice A 15 The critical point s x correspond s to the local maximum maxima Simplify your answer Use a comma to separate answers as needed Type an exact answer using radicals as needed OB There is no local maximum Select the correct choice below and if necessary fill in the answer box to complete your choice A to the local minimum minima