Calculus Questions

Question 17 a Convert the equation f t 130 1 35 to the form f t aekt k Give values accurate to three decimal places Question Help Video Message instructor

Question 15 Solve the given equation for x 35x 2 40 x

Solve for 3 14 x You may enter the exact value or round to 4 decimal places

Question 14 If e 17 then x

Question 11 Evaluate the following expressions Your answers must be exact and in simplest form a In e b eln2 C eln 3 d In 00 1 e4 Question Help Video 1 Video 2 Message instructor

Question 9 Find the logarithm log 10

Evaluate using your calculator giving at least 3 decimal places log 820 Question Help Vide

A note card company has found that the marginal cost per card of producing x note cards is given by the function below where C x is the marginal cost in cents per card Find the total cost of producing 980 cards disregarding any fixed costs C x 0 04x 76 for x 1000 The total cost is cents CB

7 Let F x 1 f dt Find F 4

For questions 6 7 8 use I Question 6 C Iz 3i 3 Question 7 C z 3i 1 Question 8 C z3i 4 C C C W C C W z 2z 1 z z C C W dz

Part 3 of 3 3 points Skipped eBook Print References Required information 3 Assign costs to the department s output specifically to the units transferred out and to the units that remain in work in process at period end Note Round Cost per EUP to 2 decimal places Cost assignment FIFO Beginning work in process To complete beginning work in process Direct materials Conversion Started and completed Direct materials Conversion Completed and transferred out Ending work in process Direct materials Conversion Total costs accounted for EUP EUP EUP Cost per EUP Cost per EUP 0 00 Cost per EUP Total cost Total cost 0 00 0 00 Total cost 0 0 0

Describe and sketch the domain of the function 2xy 2 2 y f x y X

3 is the matrix of T V V with respect to a basis H and S is the change of basis matrix from a basis 9 to H Find the matrix A of T with respect to G 1 2 2 8 33 S 1 2 B 3 4 37 A

Part 1 Re write the definite integral in terms of the variable u and remember to use the limits of integration for the function u f t Then input the antiderivative of the integrand and the limits of integration you found Part 2 Finally evaluate the original integral by evaluating the antiderivative using limits of integration from Part 1 above

3 A particle is moving with the given data Find the position of the particle a t 3 cost 2 sint s 0 0 and v 0 4

Suppose we want to evaluate the definite integral 16 r 2502 4r2 dr using the substitution u Part 2 2502 47 Part 1 Re write the definite integral in terms of the variable u and remember to use the limits of integration for the function u f r Then input the antiderivative of the integrand and the limits of integration you found Note Type your answers above in such a way that the lower limit of integration is less than the upper limit of integration

Find the area enclosed by the given curves 10x 1 x2 26 Find the area of the region between the curve y A 10 e10 B In 10 and the interval 3 x 3 of the x axis C 10 In 10 D 0

Verify the identity Simplify your answers completely 9 csc x 9 cot x sec x 9 csc x sec x sin x 1 sin x 9 cot x

Solve the multiple angle equation Enter your answers as a comma separated list Let n be any integer sec 4x 2 X

Powers of trigonometric functions are rewritten to be useful in calculus Verify the identity Simplify your answers completely 9 sin x 9 cos x 9 18 cos x 18 cos x 9 sin x 9 cos x 9 sin x E 9 1 cos x 1 cos x 918 cos x 18 cos x cos4 x

Verify that each x value is a solution of the equation 9 sec x 180 a x 9 3 sec 7 T b 9 18 5TT 3 sec 5 1 0 18 I 18 18

Verify the identity algebraically Use a graphing utility to check your result graphically 3 3 csc 0 3 cot 0 3 cos 0 sec 0

1 Find the limit Use l Hospital s Rule where appropriate If I Hospital s Rule does not apply explain why x a b lim x 01 cos x In x lim x 0 X 4118 lim xln xlm 1 1

4 Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible

Perform the addition and use the fundamental identities to simplify cos x 1 sin x tan x

Use a graphing utility to complete the table and graph the functions in the same viewing window Use both the table and the graph as evidence that y Y2 Round your answers to four decim Y cos x sin x tan x y2 sec x x Y Y2 4 3 Verify the identity algebraically 4 8 Y cos x sin x tan x cos x cos x cos x 5 3 5 8 6 3 6 8 7 3

Verify the identity Simplify your answer completely 2 sec y cos y 2 2 2 sec y cos y cos y 2

Factor the expression and use the fundamental identities to simplify Use a graphing utility to check your result graphically 2 sec x 2 sec x 2 sec x 2

Use the fundamental identities to simplify the expression Use the table feature of a graphing utility to check your result numerically 8 cot x cos x

Use the values to evaluate if possible all six trigonometric functions If an answer is undefined enter UNDEFINED 24 csc x 5 cos x sin x B tan x csc x sec x cot x 5

Let f x be the function shown in the graph below 6 Click on the graph to enlarge it Determine the absolute minimum of the function shown in the graph Answer f x Determine the absolute maximum of the function shown in the graph Answer f x 0 F Select maximum or minimum for the following The function attains a local The function attains a local The function attains a local at x 2 at x 4 at x 5 QQ y O 1 h X

etermine by direct integration the centroid of the area b X y a y kx a X

1 Below is the graph of f x Complete the following table and then draw the reciprocal of f x In the first row of the table write the key features of the given function graph In the second row explain how the key features of f x affect g x Ensure that you include the asymptotes in you sketch 10 marks Features of f x Affect of feature on 1 g x x intercepts Vertex Max min Where is the vertical asymptote of g x S d 1 Interval s where positive Interval s where negative Interval s of increase Interval s of decrease

Complete the table by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and d Round your answer to two decimal places b d 64 43 Nood Helen b C 0

Use Heron s Area Formula to find the area of the triangle Round your answer to two decimal places a 13 b 16 c 8

Consider the function f x 4 2 8 on the interval 2 7 A Find the average or mean slope of the function on this interval 4 7 4 2 Average Slope B By the Mean Value Theorem we know there exists at least one c in the open interval 2 7 such that f c is equal to this mean slope Find all values of that work and list them separated by commas in the box below List of values 9 2 14 2

4 24 81 12 30 20 10 too q 10 f x x3 x 6x 20 3 18 2 B 937 g x 6x 768 12 D 343 12

Consider the function f x 2x 18x 42x 2 with This function has an absolute minimum at the point and an absolute maximum at the point 7 x 2

7x 5 angle of the angle 7x The reference angle for IS 5 Type your answer in radians Type an exact answer using x as needed Use integers or fractions for any the expression

angle that satisties the given equation Express your answer as an inverse trigonometric function and as the measure of 0 in degrees 1 sin 0 2 Express 0 as an inverse trigonometric function 0 Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

X blem 2 Find an expression for the area under the graph of f x 11x 6 on the interval 5 10 A lim 318 D lim 818 G lim 318 Problem 2 H WI WI WI 557 i 1 2 11 5 si 10 n 10 n 5 5i n 11 5 6 5 10i n 2 11 5 0i 6 5 n 5 10i 5 n 10 6 2 n 10i n 5 5i n 216 11 5 5 6 B lim 8x n H lim n x i 1 n E lim n x n i 1 5 n n 5 5i n 11 i 6 5i n C lim n x 11 5 6 n n 2 10 n F lim n 10i n 2 11 5 10i 6 n n 10 n 5 10i n 2 11 10 6 n

Give the reference angle for angle measure 3 The reference angle is Simplify your answer Type an exact answer using as needed Use integers or fractions for any the expression

Find exact values or expressions for the six trigonometric functions of angle A Do not use a calculator A 21 29 20 sin A cos A tan A Type integers or simplified fractions csc A sec A cotA

Use the Law of Cosines to solve the triangle Round your answers to two decimal places a 13 b 6 c 18 A B C

To approximate the length of a marsh a surveyor walks x 430 meters from point A to point B Then the surveyor turns 75 and walks 220 meters to point C see figure Approximate the length AC the marsh Round your answer to one decimal place m 220 m 75

A triangular parcel of ground has sides of length 750 feet 635 feet and 585 feet Find the measure of the largest angle Round your answer to one decimal place

Choose the correct graph below OB 5 Select the correct choice below and if necessary fill in the answer box to complete your choice OA sin 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined

Watch the video that describes determining the equation for graph Click here to watch the video The function graphed to the right is of the form ya tan bx or y a cot bx for some a 0 b 0 Determine the equation of the function Half and quarter points are identified by dots

Select the correct choice below and if necessary fill in the answer box to complete your choice CODE OA sin 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined

Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle B 11 cm 97 O Law of Sines O Law of Cosines 43 Then solve the triangle Round your answers to two decimal places b CI A