Calculus Questions

Given the side length a 10 and the angle A 38 on the triangle below find the lengths of b and c and the measure of angle B Do not round during your calculations but round your final answers to one decimal place Provide your answer below B 10 C b 38 A

Find the equation of the graph given below Provide your answer below 3 2 0 0 1 3 TT 3 T TT 2TT 3 T 4TT 13 3 5TT 6TT

Use a calculator to solve the following equation for 0 on the interval csc 0 2 Find all the correct answers Report your answer as a decimal and round to three decimal places Provide your answer below

y 2 tan 4x 1 Drag the movable black point to shift the function the red points to set the vertical asymptotes and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note that only one period of the function is shown Provide your answer below 3TT 4 122 5 TT 4 4 2 2 1 4 1 0 0 3 1 2 TT 4 2 1 TQ2 3TT 4 TT

Which of the following show correct inverse trigonometric function values Select all correct answers Select all that apply arcsec 2 4 arcsec 2 3 arccsc 1 0 arcesc 1 arccot 4 3 3 10 3 T arccot

Given the triangle below find the angle 0 in degrees Round to one decimal place 8 0 7

et C be the positively oriented square with vertices 0 0 1 0 1 1 0 1 Use Green s Theorem to evaluate the line integral J10y z dz 10x ydy

Given the side length b 9 and the angle A 73 on the triangle below find the lengths of a and c and the measure of angle B Do not round during your calculations but round your final answers to one decimal place B Provide your answer below a 73 A 9 C

y cot 5x Drag the movable red point to set the asymptotes for one period of the given function Also place the blue point at the correct set of coordinates You may click on a point to verify its coordinates Provide your answer below TT 5 7 6 5 4 3 2 14 0 2 3 4 TT 5 2T 5 4TT 5 6m 5

Find the particular antiderivative of the following derivative that satisfies the given condition dR dt 64 1 R 4 50

Find the indefinite integral Check by differentiation 12e 10 dz

Given that cot x 1 what is cot x

Choose one point in the figure that is NOT in the domain of cot x defined in the Provide your answer below TT 12 TTA TT 2 4 0 0 TT 2 12 TT

2 Simplify the following a sinx cos x secx cscx sin cos x b cos x sinx 4 tanx secx 2 secx c 6 tanx secx 2 secx sin x cos x d sin x cos x 1 e sin x cos x secx sinx sinx cos x 1 cos x g tanx 2 cosx sinx sinx 1 cos x sin u 3 5 and and 3 Assuming that evaluate each of the following exactly a cos u v c tan u v b sin u v d cos u v sin v 4 5 that u and v are between 0 am

a sec x 2 tar x 2 cox 2 cs x 2 a 5 Find the exact value of sin 26 cos 24 tan 24 10 sin 10 b cos p b tan o d in quadrant IV 3 5 in quadrant III 5 12 in quadrant IV

6 Prove the following 1 cosx sinx cosx 1 a sinx cosx sinx cos x 1 cos x b sin x 2csc x 1 c cos x cotx cot x cos x 1 sinx secx tanx d 1 sinx e sec x tan x tan x sec x

1 Evaluate a sin sin 1 sin cos d 4 tanx secx 2 secx c 6 tanx secx 2 secx sin x cos x d sin x cos x 1 e sin x cos x secx sinx b 2 Simplify the following a sinx cos x secx cscx sin cos x b cos x sinx i sinxcosx 1 cos x sinx o tanx 1 COS X sin tan 2 cosx sinx 12 e sin cos x 3 c cos tan 3 tan sin 9 f

sin u 5 and and 3 Assuming that evaluate each of the following exactly a cos u v c tan u v b sin u v d cos u v sin v tan x b d cs x 27 5 that u and v are between 0 and 2 4 Find an equivalent expression for each of the following a sed x c cof x 27

A pizza pan is removed at 1 00 PM from an oven whose temperature is fixed at 450 F into a room that is a constant 71 F After 5 minutes the pizza pan is at 300 a At what time is the temperature of the pan 125 F b Determine the time that needs to elapse before the pan is 200 c What do you notice about the temperature as time passes a The temperature of the pan is 125 F at PM

Provide your answer below TT TT 2 2 1 0 1 2 In the domain of f x cot x defined in the interval X T TT 2 3 4 0 TT

Find all of the following that applies then sketch the graph a Classify the type of conic section as a circle parabola ellipse or hyperbola b Center c Vertex or vertices d Focus or foci e Directrix parabola only f Eccentricity ellipse and hyperbola only g Sketch and label the graph 1 4x 9y 32x 36y 64 0

figure Provide your answer below A 0 TT 2 3 2 1 0 1 2 3 0 0 TT 2 Wild Value X does I X Choose the points in the

For matrices A B Mnxn F we say that A and B are unitarily similar if there exists a unitary matrix U E Mnxn F such that U AU B Note that since U is unitary U U so being unitarily similar is a special case of being similar Let A B Mnxn F be unitarily similar Use proof by induction to show that A and B are unitarily similar for all kEN

Given that tan x 2 what is tan x

Higgst ne po Provide your answer below 2 311 2 TT 2 6 4 0 2 0 0 TT 2 m 3m 2 27 X ined in the interval 27 X 0

On the graph of f x cot x and the interval for what values of X does Provide your answer below TT 3 TT 2 2 1 1 2 0 0 1 2 3 2 0 TT 2 TT

the origin with the given focus or directrix 1 Focus 6 0 2 Focus 0 4 3 Directrix x 3 4 Directrix y 5 5 Focus 0 7 6 Directrix x 9 7 Focus 1 0 8 Directrix x 1 9 Focus 2 0

Sketch the solid and a typical disk or washer y 4 2 4 y 4 2 4 4 06 4 2 4 y y 2 4

Find the area of the shaded region x y 10 y 75 4 15 2 30 20 x 5y y 10 10 5 6 y X

Ow dy X and ow dy 2 2 at the point w x y z 12 2 1 2 if w 2x y 2yz 2z and x y 2 9

ow and b w 2 2 2 at the point x y z 2 1 2x if w x y z and y sin z z sin x 0

The Taylor series for f x x at 2 is cn x 2 3 Find the first few coefficients CO C1 C2 C3 C4 n 0

The Maclaurin series of the function f x 4x sin 3x can be written as f x Cnxn n 0 where a few of the coefficients are C3 C4 C5 C6 C7 www

Suppose that 3x 2y 1 and x tcos 8 Find F and at dy

Find the area of the shaded region 1 y 8 00 6 4 2 1 1 y 5x x y 2x 2 3 3 6 4 5 LE 6 X

So Determine whether the improper integral converges or diverges If it converges find its value da Converge 2 Diverge Converge 3 Converge 1

When writing a rational function as a power series if the numerator has degree one less than the denominator the partial fraction method will work True O False

Use a substitution to find You must show your work to receive full credit In a Edit Format Table dx

Use an integration formula to find f O 16 O w a ln 164 cos O 16 r 4 In V x 1 16 4 C 3 4 16 2 C C 16 x dx

olve the following initial value problem y 4y 5y t 2 8 t y 0 1 y 0 2

Use Half Angle or Double Angle Formula to find f sin 5xdx You must show your work to receive full credit

Use partial fractions to evaluate d dx O 5 ln 2 1 6 C O In x 2 x 3 C O In C O In C 5 x x 6

Use Integration by Parts Formula to find e dx Or e 2re e C O e 2re e C e 2xe 2e C

Use a substitution to find f sec 0 tan de sec 0 Os C O4 sec 0 tan0 C

5 Find the number of sides for a polygon whose sum of the measures of its interior angles is a 900 b 1260

Use a substitution to evaluate the definite integral 0 1 In 3 01 In 2 Cos 11 sin dr

Assume a is opposite side a is opposite side b and y is opposite side c Solve each triangle for the unknown sides and angles if possible If there is more than one possible solution give both 21 y 41 2 a 2 49 b 3 13 23 a 120 b 6 c 7 22 B 58 7 a 10 6 c 15 7 24 y 115 a 18 b 23

Use a substitution to find fre 1 da O e 1 2x e C 0 0 O e 41 C

Use a substitution to evaluate the definite integral cos x da Osin 1 Ocos 1 sin 1

3 15pts Evaluate cos B where cos 3 4 with in 2th Quadrant and sin 5 7 with B in Quadrant II 4 16 pts Find an equivalent expression for cot