Calculus Questions

Find the angles of AABC given that 11 b 26 and c 20 Round your answers to the nearest tenth of a degree B 11 C 20 26 A

Given that AABC has mA 63 b 9 and c 11 find the remaining side length a and angles B and C rounded to the nearest tenth Provide your answer below A 63 9 11 C a B

Find the angles of AABC given that a 11 b 20 and c 18 Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles B 18 11 C 20

Find the missing side length and angles of AABC given that mZC 126 a 7 and b 11 A Select the correct answer below Oc 15 1 A 19 5 and B 34 5 Oc 16 1 A205 and B 33 5 Oc 16 1 A 19 5 and B 34 5 Oc 15 1 A 205 and B 33 5 11 C 126 C 7 B

An airplane started at point X traveled 320 miles to point Y adjusted its route and traveled another 400 miles to point Z If the airplane is currently 599 miles from its starting position at point X by how many degrees did it adjust its route at point Y Round your answer to the nearest degree if necessary Do not enter the degree symbol Z 400 Y 599 320

Chris invests 15 000 at 7 simple interest for 19 years Round your answers to the nearest cent How much interest is earned over the 19 year period How much is in the account at the end of the 19 year period

970 9 2m 9 4 I 97 4 Step 2 We now must find a pair of polar coordinates that represents the same point with a radius r 0 Recall that for a negative radius the resulting point is on the same line through the origin as the point with positive radius it is the same distance from the origin but it is on opposite sides of the origin 5 T 9 The angle of the direction opposite the point is 50

Sketch the curve with the given polar equation by first sketching the graph of r as a function of 8 in Cartesian coordinates 2 4 sin 28 y 3 2 8 X 3 3 2 2 2 3 O Need Help Read It Watch It 2 y 2 2 2 WA X 1 5 1 0 0 5 y 1 5 1 0 0 5 0 5 1 0 1 5 0 5 1 0 1 5 X 1 y 2 1 1

10 Find the exact area of the surface z x y in the 1st octant that lies between the cylinders x y 2 a x y 3 0 0 1 5 0 5 1 0 1 0 0 5 1 5 0 0 2

4 How can we use transformations to manipulate the shape position and behavior of a polynomial function and how do these changes impact its graphical representation and algebraic properties

3 For the following function use the key points of the parent function to perform transformations Graph the parent and transformed function Write the equation of the transformed function Include a table of values for the parent and transformed function f x x g x f x 1 2 20 18 16 14 12 10 0 8 10 12 14 16 16 le

Sum of x 1 to infinity 3 x 3x 0 5 9 x determine if converges or diverges

2 For the following function complete the table and sketch a graph h x x 4 x 3 Degree Leading Coefficient End Behaviour x intercepts y intercept

8 TI Pitt Lake is a freshwater lake In a daily 24 hour period the highest tide is traditionally at 11 00am reaching 5 8m and the lowest tide is traditionally at 11 00 pm reaching only 0 4m These are seasonal times and heights a Determine a cosine function that gives the tidal height of the lake h in terms of the hours after midnight t b Create a sketch of this function sketch first label after What is th 20

Find the angles of AABC given that a 12 b 21 and c 19 Round your answers to the nearest tenth of a degree Provide your answer below C A 21 7 19 12 B

81 Christina travels on one street for 1 750 meters She then turns and travels on another street for 1 821 meters This route is represented in the figure by the sequence of points X Y Z According to the angle shown in the figure and the given information what is the distance to the nearest meter from Christina s house to school represented by the line from X to Z in the figure Provide your answer below X 1750 129 Y 1821 Z

2z Use the Divergence theorem to find the outward flux of F In x y i tz tan zx y k across the boundary of the region D which is the thick walled cylinder 1 x y 2 1 z 2

1 point Find the curvature t of the curve r r t 2 sin t i 2 sin t j 1 cost k

Q49 Evaluate log3 54 log162 3 log3 486 log18 3

Problem 3 A QR decomposition is a decomposition of a matrix A into a product A QR of an orthonormal matrix Q and an upper triangular matrix R Write a command that takes a matrix A as input and computes a QR decomposition of the matrix Refer to Section 4 3 of the Olver text for details on a possible algorithm for decomposing A into the form QR

se Newton s method with the specified initial approx ation x to find x3 the third approxim x 1 0 X 2 X X3 1 53912 2

a What is a sequence OA sequence is an ordered list of numbers OA sequence is the sum of an ordered list of numbers A sequence is the product of an ordered list of numbers A sequence is the sum of an unordered list of numbers A sequence is an unordered list of numbers b What does it mean to say that lim nan 8 O The terms an approach infinity as 8 approaches n O The terms an approach 8 as n becomes large O The terms an approach infinity as 8 approaches n O The terms an approach infinity as n become large The terms a s an approach 8 as n becomes small c What does it mean to say that lim n O The terms an approach zero as n becomes large O The terms a become large as n becomes small O The terms a become small as n becomes small become small as n becomes large become large as n becomes large O The terms an O The terms an

List the first five terms of the sequence 1 a a3 4 a5 cos n an

Find a Cartesian equation for the curve r 3 cos 8 0 x Identify the curve O circle Olima on Oline O ellipse O hyperbola

If 19 200 cm2 of material is available to make a box with a square base and an open top find the largest possible volume of the box Step 1 We are given that the box has a square base and an open top Let b represent the length of the box s base and let h represent the height of the box each measured in cm Let V represent volume of the box measured in cm Writing an equation for Vin terms of b and h gives us the following V 256000 cm3 X Let S represent the surface area of the box measured in cm2 Writing an equation for S in terms of b and h gives us the following s b 4bh cm

Graph the following iction f x Label the vertical asymptote State the domain and range of the function f x log x Graph the given function f x Label the vertical asymptote Choose the correct graph The domain of this logarithmic function is Type your answer in interval notation The range of this logarithmic function is Type your answer in interval notation COL A O C f x f x B O D Af x G E G C E G

Find two numbers whose difference is 54 and whose product is a minimum Step 1 If two numbers have a difference of 54 and we let x represent the smaller of these two numbers then the larger of these two numbers is given by the foll 27 X

nd the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative f x x 9 2

f x x 27x 61 Identify all the relative minimum points Select the correct choice below and if necessary fill in the answer box to complete your choice OA The relative minimum point s is are Simplify your answer Use integers or fractions for any numbers in the expression Type an ordered pair Use a comma to separate answers as needed OB There are no relative minimum points Identify all the relative maximum points Select the correct choice below and if necessary fill in the answer box to complete your choice OA The relative maximum point s is are Simplify your answer Use integers or fractions for any numbers in the expression Type an ordered pair Use a comma to separate answers as needed OB There are no relative maximum points Graph the function Choose the correct graph below OA OB SELLE Q Q O C Q OD

Find the antiderivative F of f that satisfies the given condition Check your answer by comparing the graphs of f and F f x 2ex 8x F 0 5 F x I

Find f f x f x 4 6x 24x f 0 2 f 1 12

f x x 9x Tema of the function List each extremum along with the x value at which it occurs Identify intervals over which the function is increasing and over which it is decreasing Then sketch a graph of the function Describe any relative extrema Select the correct choice below and if necessary fill in the answer box es within your choice and there are no relative minimum points pair using integers or fractions Use a comma to separate answers as needed OA The relative maximum point s is are Simplify your answer Type an ordered OB The relative minimum point s is are Simplify your answer Type an ordered OC The relative minimum point s is are and there are no relative maximum points pair using integers or fractions Use a comma to separate answers as needed and the relative maximum point s is are Simplify your answers Type ordered pairs using integers or fractions Use a comma to separate answers as needed OD There are no relative minimum points and there are no relative maximum points Identify any intervals over which the function is increasing or decreasing Select the correct choice below and fill in the answer box es within your choice OA OA The function f x is increasing over the interval s and is not decreasing anywhere Type your answer in interval notation Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed OB The function f x is decreasing over the interval s and is not increasing anywhere Type your answer in interval notation Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed OC The function f x is increasing over the interval s and decreasing over the interval s Type your answers in interval notation Use integers or fractions for any numbers in the expressions Use a comma to separate answers as needed Choose the correct graph below 200 Ay Q OB Ay 200 200 Q Q G O C 200 Ay N Q O D 7

Now we must find f x which is given by the general antiderivative of f x 18x2 C We note that f x is the sum of two functions h x 18x and b x C such that f x h x b x This means that f x will be given by the following where H x is the general antiderivative of h x B x is the general antiderivative of b x and D is an arbitrary constant f x H x B x D Furthermore we note that h x 18x2 is the product of a constant and a function k x x such that h x 18k x Finally we note that b x C is a constant function and can be written in the form b x Cx Applying the formulas described in this step and those used in the previous step we can now state the following letting D represent the arbitrary constant Do not add any additional constants f x 18x C 18 f x 18 Cx D To conclude give an equation for f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x

Assume that the equation exyz sin x y z implicitly defines z as a function of x y We will find using two methods z x a Go through and implicitly take partial derivatives with respect to x on both sides of the given equation treating z as a function of x and treating y as constant and remembering to use the chain rule when necessary Then solve for This is the method you learned in Calc I x b i Ignore the above equation for a moment and consider the general case where some equation F x y z 0 implicitly defines z as a function of x y Use the multivariable chain rule to find a general formula for x z ii Now use the formula you found to find az for the above example x

Consider the curve 1 1 t Determine B 0 r t i t t j ln 1 t k

A particle is moving with the given data Find the position of the particle s a t 2t 9 s 0 5 v 0 3 t

The values of y yo and t are given For an equation of the form y yoekt give the exact value of k in terms of natural logarithms Yo 120 t 3 y 40 k 0 se integers or fractions for any numbers in the expression www

Two artillery bases are located at the points P and R represented in the figure Each of the bases locates an enemy airplane at point Q and measures the angles of elevation to the airplane Given the elevation angles in the figure and the fact that the two bases are 662 meters apart what is the distance in meters from the base at point R to the airplane Round your answer to the nearest tenth if necessary

A large room has a temperature of 70 degrees Fahrenheit When a cup of tea is brought into the room the tea has a 70 represents the situation where t is time in temperature of 120 degrees Fahrenheit The function f t minutes C is a constant and k is a constant Cel kt After 3 minutes the cup of tea has a temperature of 100 degrees What will be the temperature of the tea in degrees Fahrenheit after 5 minutes Round your answer to the nearest tenth and do not include units

3 Integrate G x y z x over the parabolic cylinder y x 0 x 2 Write the integral G x y z do as a double integral S SS G x y z do SSO dx dz S 0 z 1

Anne wants to know the distance across a mountain canyon from point Z to point Y shown in the figure point Z Anne chooses the point X and measures the angles between each of these points and the point on the other side of the canyon The measures of these angles are shown in the figure If the distance from point X to point Z is 75 feet what is the distance across the canyon from point Z to point Y in feet Round your answer to the nearest tenth if necessary Y 958

In APQR sin P sin Q 3 and p 15 Find the side lengt Select the correct answer below 09 9 1 O q 75 09 6 O q 31 09 15 O q 30

In AABC sin B sin C and b 12 Find the side length c Select the correct answer below O c 1 2 Oc 2 4 O c 9 O c 42 c 24

Two lookout towers have been set up to keep a watch on forest fires The two towers are represented by the points X and Z in the figure A fire is spotted at point Y and each tower measures the angle from the opposite tower to the fire as shown in the figure If the distance between the two towers is 442 meters what is the distance in meters from the tower at point Z to the fire 600 1000 Y

Use the definition of Taylor series to find the Taylor series centered at c for the function f x COS X f x 8 n 0 C T 4 n X 4 cos n 2an COS n

Tutorial Exercise Find the Maclaurin series for the function f x cos 9x Step 1 To find Maclaurin series for the function f x cos 9x recall the power series for the elementary function cos x COS X 00 1 x2n 2n

Two artillery bases are located at the points K and M represented in the figure Each of the bases locates an enemy airplane at point L and measures the angles of elevation to the airplane Given the elevation angles in the figure and the fact that the two bases are 485 meters apart what is the distance in meters from the base at point M to the airplane L

In AABC sin A 2 sin B 1 and a 8 Find the side length b Select the correct answer below Ob 15 Ob 4 Ob 28 b 3 7 Ob 14 Ob

8 Taylor s theorem generates a power series from a function using the formula f x f n c x c n n 0 True O False

Find y and y y y y In x 9 x 9 x 2 X 9 x 2